RD SHARMA Solutions for Class 10 Maths Chapter 13 - Areas Related to Circles

Chapter 13 - Areas Related to Circles Exercise 13.69

Question 1

If the circumference and the area of a circle are numerically equal, then diameter of the circle is

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 1

Correct Option :- (D)

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 2

If the difference between the circumference and radius of a circle is 37 cm., then using π = Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles, the circumference (in cm) of the circle is

(a) 154

(b) 44

(c) 14

(d) 7 

Solution 2

According to the question,

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Circumference of a circle = Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

 = Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

 = 44 cm 

Question 3

A write can be bent in the form of a circle of radius 56 cm. If it is bent in the form of a square, then its area will be

(a) 3520 cm2

(b) 6400 cm2

(c) 7744 cm2

(d) 8800 cm2

Solution 3

Correct option (c)

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 4

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 4

correct option - (c)

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 5

A circular park has a path of uniform width around it. The difference between the outer and inner circumferences of the circular path is 132 m. Its width is

(a) 20 m

(b) 21 m

(c) 22 m

(d) 24 m

Solution 5

correct option - (b)

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 6

The radius of a wheel is 0.25 m. The number of revolutions it will make to travel a distance of 11 km will be

(a) 2800

(b) 4000

(c) 5500

(d) 7000

Solution 6

Correct Option: d

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 7

The ratio of the outer and inner perimeters of a circular path is 23:22. If the path is 5m wide, the diameter of the inner circle is 

(a) 55m

(b) 110 m

(c) 220 m

(d) 230 m

Solution 7

Correct Option: (c)

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 8

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 8

Correct option - (c)

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 9

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 9

Correct option (c)

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 10

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 10

Correct Option ( d )

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 11

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 11

Correct option (a)

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 12

The perimeter of a triangle is 30 cm and the circumference of its incircle is 88 cm. The area of the triangle is

a. 70 cm2

b. 140 cm2

c. 210 cm2

d. 420 cm2 

Solution 12

Let r be the radius of the circle.

2pr = 88

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Perimeter of a triangle = 30 cm

Semi-perimeter = 15 cm

Hence,

Area of a triangle = r × s …(r = incircle radius, s =semi perimeter)

= 14 × 15

= 210 cm2 

Question 13

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 13

Correct option - (c)

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Chapter 13 - Areas Related to Circles Exercise 13.70

Question 1

If the circumference of a circle increases from 4π to 8π, then its area is

(a) halved

(b) doubled

(c) tripled

(d) quadrupled

Solution 1

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 2

If the radius of a circle is diminished by 10%, then its area is diminished by

(a) 10%

(b) 19%

(c) 20%

(d) 36%

Solution 2

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 3

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 3

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 4

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 4

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 5

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 5

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 6

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 6

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 7

If the perimeter of a semi-circular protractor is 36 cm, then its diameter is

(a) 10 cm

(b) 12 cm

(c) 14 cm

(d) 16 cm

Solution 7

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 8

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 8

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 9

If the perimeter of a sector of a circle of radius 6.5 cm is 29 cm, then its area is

(a) 58 cm2

(b) 52 cm2

(c) 25 cm2

(d) 56 cm2

Solution 9

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 10

If the area of a sector of a circle bounded by an arc of length 5π cm is equal to 20π cm, then its radius is

(a) 12 cm

(b) 16 cm

(c) 8 cm

(d) 10 cm

Solution 10

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 11

The area of the circle that can be inscribed in a square of side 10 cm is

(a) 40 π cm2

(b) 30 π cm2

(c) 100 π cm2

(d) 25 π cm2

Solution 11

Correct option: (d)

Diameter of circle = side of square

2r = 10

r = 5 cm

Area of circle = πr2 = 25 π cm2

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 12

If the difference between the circumference and radius of a circle is 37 cm, then its area is

(a) 154 cm2

(b) 160 cm2

(c) 200 cm

(d) 150 cm2

Solution 12

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Chapter 13 - Areas Related to Circles Exercise 13.71

Question 1

The area of a circular path of uniform width h surrounding a circular region of radius r is

(a) π (2r + h) r

(b) π (2r + h) h

(c) π (h + r) r

(d) π (h + r) h

Solution 1

Correct option: (b)

Inner radius = r

outer radius = r + h

area of shaded region = area of outer circle - area of inner circle

= π (r + h)2 - πr2

= π {(r + h)2 - r}

= π (r + h - r) (r + h + r)

= π (2r + h) h

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 2

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 2

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 3

The area of a circle whose area and circumference are numerically equal, is

(a) 2π sq. units

(b) 4π sq. units

(c) 6π sq. units

(d) 8π sq. units

Solution 3

Correct option: (b)

area = circumference

πr2 = 2πr

r = 2 units

area = πr2

       = 4π sq. units

Question 4

If diameter of a circle is increased by 40%, then its area increases by

(a) 96%

(b) 40%

(c) 80%

(d) 48%

Solution 4

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 5

In figure, the shaded area is

(a) 50 (π - 2) cm2

(b) 25 (π - 2) cm2

(c) 25 (π + 2) cm2

(d) 5 (π - 2) cm2

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 5

** img pending

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 6

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

 

Solution 6

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 7

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 7

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Chapter 13 - Areas Related to Circles Exercise 13.72

Question 1

If the area of a sector of a circle bounded by an arc of length 5π cm is equal to 20π cm2, then the radius of the circle is

(a) 12 cm

(b) 16 cm

(c) 8 cm

(d) 10 cm

Solution 1

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 2

In Figure, the ratio of the areas of two sectors Sand S2 is

(a) 5 : 2

(b) 3 : 5

(c) 5 : 3

(d) 4 : 5

Solution 2

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 3

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 3

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 4

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 4

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 5

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 5

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Chapter 13 - Areas Related to Circles Exercise 13.73

Question 1

In figure, the area of the shaded region is

(a) 3π cm2

(b) 6π cm2

(c) 9π cm2

(d) 7π cm2

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 1

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 2

If the perimeter of a circle is equal to that of a square, then the ratio of their areas is

(a) 13 : 22

(b) 14 : 11

(c) 22 : 13

(d) 11 : 14

Solution 2

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 3

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 3

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 4

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 4

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 5

If a chord of a circle of radius 28 cm makes an angle of 90° at the centre, then the area of the major segment is

(a) 392 cm2

(b) 1456 cm2

(c) 1848 cm2

(d) 2240 cm2

Solution 5

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 6

If area of a circle inscribed in an equilateral triangle is 48π square units, then perimeter of the triangle is

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 6

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Chapter 13 - Areas Related to Circles Exercise 13.74

Question 1

The hour hand of a clock is 6 cm long. The area swept by it between 11.20 am and 11.55 am is

(a) 2.75 cm2

(b) 5.5 cm2

(c) 11 cm2

(d) 10 cm2

Solution 1

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 2

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 2

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 3

If the area of circle is equal to the sum of the areas of two circles of diameters 10 cm and 24 cm, then diameter of the larger circle (in cm) is

(a) 34

(b) 26

(c) 17

(d) 14

Solution 3

Correct option: (b)

radius of Circle = 5 cm

area = π (5)2

       = 25 π

rdius of circle 2 = 12 cm

area = π (12)2

       = 144 π

area of larger circle = 144 π + 25π

                            = 169 π

πr2 = 169 π

r2 = 169

r = 13

diameter = 2r

              = 26

Question 4

If Π is taken as 22/7, the distance (in metres) covered by a wheel of diameter 35 cm, in one revolution, is

(a) 2.2

(b) 1.1

(c) 9.625

(d) 96.25 

Solution 4

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 5

ABCD is a rectangle whose three vertices are B(4, 0), C(4, 3) and D(0, 3). The length of one of its diagonals is

(a) 5

(b) 4

(c) 3

(d) 25

Solution 5

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

 

Question 6

Area of the largest triangle that can be inscribed in a semi-circle of a radius r units is

 

a. r2 sq. units

b. Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

c. 2r2 sq. units

d. Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 6

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

 

 

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 7

If the sum of the areas of two circles with radii r1 and r2 is equal to the area of a circle of radius r, then

 

a. r = r1 + r2

b. Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

c. r1 + r2 < r

d. Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 7

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 8

If the sum of the circumference of two circles with radii r1 and r2 is equal to the circumference of a circle of radius r, then

 

a. r = r1 + r2

b. r1 + r2 > r

c. r1 + r2 < 2

d. None of these

Solution 8

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 9

If the circumference of a circle and the perimeter of a square are equal, then

 

 

a. Area of the circle = Area of the square

b. Area of the circle < Area of the square

c. Area of the circle > Area of the square

d. Nothing definite can be said

Solution 9

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 10

If the perimeter of a circle is equal to that of a square, then the ratio of their areas is

 

a. 22 : 7

b. 14 : 11

c. 7 : 22

d. 11 : 14

Solution 10

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Chapter 13 - Areas Related to Circles Exercise Ex. 13.1

Question 1

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 1

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 2

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 2

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 3

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 3

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 4

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 4

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 5

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 5

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 6

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 6

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 7

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 7

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 8

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 8

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 9

Find the radius of a circle whose circumference is equal to the sum of the circumference of two circles of radii 15 cm and 18 cm.

Solution 9

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 10

The radii of two circles are 8 cm and 6 cm respectively. Find the radius of the circle having its area equal to the sum of the areas of the two circles.

Solution 10

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 11

The radii of two circles are 19 cm and 9 cm respectively. Find the radius and area of the circle which has its circumference equal to the sum of the circumferences of the two circles.

Solution 11

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

 

Area of a circle = πr2 = (22/7) × 28 × 28 = 2464 cm2

Question 12

The area of a circular playground is 22176 m2. Find the cost of fencing this ground at the rate of Rs. 50 per metre.

Solution 12

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 13

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 13

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 14

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 14

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles
Question 15

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 15

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles
Question 16

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 16

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 17

A park is in the form of a rectangle 120 m x 100 m. At the centre of the park there is a circular lawn. The area of park excluding lawn is 8700 m2. Find the radius of the circular lawn. (Use = 22/7).

Solution 17

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles
Question 18

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 18

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 19

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 19

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles
Question 20

An archery target has three regions formed by three concentric circles as shown in figure. If the diameters of the concentric circles are in the ratio 1 : 2 : 3, then find the ratio of the areas of three regions.

 

 

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 20

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

 

 

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 21

The wheel of a motor cycle is of radius 35 cm. How many revolutions per minute must the wheel make so as to keep a speed of 66 km/hr?

Solution 21

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 22

A circular pond is 17.5 m in diameter. It is surrounded by a 2 m wide path. Find the cost of constructing the path at the rate of Rs.25 per m2.

Solution 22

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 23

A circular park is surrounded by a road 21 m wide. If the radius of the park is 105 m, find the area of the road.

Solution 23

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 24

A square of diagonal 8 cm is inscribed in a circle. Find the area of the region lying inside the circle and outside the square.

Solution 24

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

 

 

 

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 25

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 25

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

 

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 26

Find the area enclosed between two concentric circles of radii 3.5 cm and 7 cm. A third concentric circle is drawn outside the 7 cm circle, such that the area enclosed between it and the 7 cm circle is same as that between the two inner circles. Find the radius of the third circle correct to one decimal place.


Solution 26

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To CirclesRd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 27

A path of width 3.5 m runs around a semi-circular grassy plot whose perimeter is 72 m. Find the area of the path. (Use π = 22/7)

Solution 27

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

 

 

 

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 28

A circular pond is of diameter 17.5 m. It is surrounded by a 2 m wide path. Find the cost of constructing the path at the rate of Rs. 25 per square meter (π = 3.14)

Solution 28

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 29

The outer circumference of a circular race-track is 528 m. The track is everywhere 14 m wide. Calculate the cost of levelling the track at the rate of 50 paise per square metre (Use Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles = 22/7).

Solution 29

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 30

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 30

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 31

Prove that the area of a circular path of uniform width h surrounding a circular region of radius r is Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles h (2r + h).

Solution 31

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Chapter 13 - Areas Related to Circles Exercise Ex. 13.2

Question 1

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 1

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles
Question 2

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 2

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 3

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 3

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 4

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 4

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 5

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 5

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 6

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 6

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 7

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 7

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 8

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 8

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 9

The area of a sector of a circle of radius 5 cm is 5Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles cm2. Find the angle contained by the sector.

Solution 9

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 10

Find the area of the sector of a circle of radius 5 cm, if the corresponding arc length is 3.5 cm.

Solution 10

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 11

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 11

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 12

The perimeter of a scetor of a circle of radius 5.7 m is 27.2 m. Find the area of the sector.

Solution 12

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles



Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 13

The perimeter of a certain sector of a circle of radius 5.6 m is 27.2 m. Find the area of the sector.

Solution 13

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 14

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 14

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 15

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 15

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 16


Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 16

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 17

A sector of 56o cut out from a circle contains area 4.4 cm2. Find the radius of the circle.

Solution 17

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 18

Area of a sector of central angle 200° of a circle is 770 cm2. Find the length of the corresponding arc of this sector.

Solution 18

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 19

The length of minute hand of a clock is 5 cm. Find the area swept by the minute hand during the time period 6:05 am and 6:40 am.

Solution 19

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 20

The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes.

Solution 20

 

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles


 

*Answer does not match with textbook answer.

Question 21

In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. Find

 

(i) the length of arc

(ii) area of the sector formed by the arc. (use π = 22/7)

Solution 21

 

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles



Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles


Question 22

From a circular piece of cardboard of radius 3 cm two sectors of 90° have been cut off. Find the perimeter of the remaining portion nearest hundredth centimeters. (Take π = 22/7)

Solution 22

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

 

 

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

*Note: Answer given in the book is incorrect.

Question 23

The area of a sector is one-twelfth that of the complete circle. Find the angle of the sector.

Solution 23

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

 

 

 

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 24

AB is a chord of a circle with centre O and radius 4 cm. AB is of length 4 cm. Find the area of the sector of the circle formed by chord AB.

Solution 24

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles
Question 25

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 25

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles
Question 26

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 26

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To CirclesRd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 27

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 27

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles


Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Chapter 13 - Areas Related to Circles Exercise Ex. 13.3

Question 1

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 1

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 2

A chord PQ of length 12 cm subtends an angle of 120o at the centre of a circle. Find the area of the minor segment cut off by the chord PQ.

Solution 2

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 3

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 3

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 4

A chord 10 cm long is drawn in a circle whose radius is Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles cm. Find area of both the segments. (Take Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles = 3.14).

Solution 4

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

 

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 5

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 5

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 6

Find the area of the minor segment of a circle of radius 14 cm, when the angle of the corresponding sector is 60°.

Solution 6

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 7

A chord of a circle of radius 10 cm subtends an angle of 90° at the centre. Find the area of the corresponding major segment of the circle. (Use π = 3.14)

Solution 7

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To CirclesNote: Question modified

Question 8

The radius of a circle with centre O is 5 cm. Two radii OA and OB are drawn at right angles to each other. Find the areas of the segments made by the chord AB. (π = 3.14)

 

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

 

 

Solution 8

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 9

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 9

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 10

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 10

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Chapter 13 - Areas Related to Circles Exercise Ex. 13.4

Question 1

A plot is in the form of the form of a rectangle ABCD having semi-circle on BC as shown in Fig., If AB = 60 m and BC = 28 m, find the area of the piot.

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 1

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 2

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 2

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 3

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 3

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 4

A rectangular piece is 20 m long and 15 m wide. Form its four corners, quadrants of radii 3.5 m have been cut. Find the area of the remaining part.

Solution 4

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 5

In fig., PQRS is a square of side 4 cm. Find the area of the shaded region.

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 5

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 6

Four cows are tethered at four corners of a square plot of side 50 m, so that they just cannot reach one another. What area will be left ungrazed?

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 6

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 7

A cow is tied with a rope of length 14 m at the corner of a rectangular field of dimensions 20m × 16m, find the area of the field in which the cow can graze.

Solution 7

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

 

 

 

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 8

A calf is tied with a rope of length 6 m at the corner of a square grassy lawn of side 20 m. If the length of the rope is increased by 5.5 m, Find the increase in area of the grassy lawn in which the calf can graze.

Solution 8

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

 

 

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 9

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 9

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 10

A rectangular park is 100 m by 50 m. It is surrounded by semi-circular flower beds all round. Find the cost of levelling the semi-circular flower beds at 60 paise per square metre (Ise Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles = 3.14).

Solution 10

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles


Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 11

The inside perimeter of a running track (shown in Fig.) is 400 m. The length of each of the straight portion is 90 m and the ends are semi-circles. If the track is everywhere 14 m wide, find the area of the track. Also, find the length of the outer running track.

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 11

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 12

Find the area of Fig., in square cm, correct to one place of decimal. (Take π = 22/7).

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 12

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 13

From a rectangular region ABCD with AB = 20 cm, a right angle AED with AE = 9 cm and DE = 12 cm, is cut off. On the other end, taking BC as diameter, a semicircle is added on outside the region. Find the area of the shaded region. (π = 22/7)

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 13


Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 14

From each of the two opposite corners of a square of side 8 cm, a quadrant of a circle of radius 1.4 cm is cut. Another circle of radius 4.2 cm is also cut from the centre as shown in Fig. Find the area of the remaining (shaded) portion of the square. (Use π = 22/7)

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 14

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 15

ABCD is a rectangle with AB = 14 cm and BC = 7 cm. Taking DC, BC and AD as diameters, three semi-circles are drawn as shown in the figure. Find the area of the shaded region.

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles
Solution 15

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 16

ABCD is rectangle, having AB = 20 cm and BC = 14 cm. Two sectors of 180° have been cut off. Calculate :

(i) the area of the shaded region.     (ii) the length of the boundary of the shaded region.

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles
Solution 16

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 17

The square ABCD is divided into five equal parts, all having same area. The central part is circular and the lines AE, GC, BF and HD lie along the diagonals AC and BD of the square. If AB = 22 cm, find:

(i) the circumference of the central part.   (ii) the perimeter of the part ABEF.

 

         

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 17

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 18

In figure, find the area of the shaded region.

(Use π = 3.14)

 

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 18

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

 

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 19

OACB is a quadrant of a circle with centre O and radius 3.5 cm. If OD = 2 cm, find the area of the (i) quadrant OACB (ii) shaded region.

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 19

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 20

A square OABC is inscribed in a quadrant OPBQ of a circle. If OA = 21 cm, find the area of the shaded region.

 

 

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

 

 

Solution 20

 

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 21

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 21

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 22

OE = 20 cm. In sector OSFT, square OEFG is inscribed. Find the area of the shaded region.

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles
Solution 22
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles
Question 23

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 23

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 24

A circle is inscribed in an equilateral triangle ABC of side 12 cm, touching its sides (fig.,). Find the radius of the inscribed circle and the area of the shaded part.

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 24

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 25

In fig., an equilateral triangle ABC of side 6 cm has been inscribed in a circle. Find the area of the shaded region. (Take Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles = 3.14).

 

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 25

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

*Answer is not matching with textbook.

Question 26

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles
Solution 26

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 27

Find the area of a shaded region in the given figure, where a circular arc of radius 7 cm has been drawn with vertex A of an equilateral triangle ABC of side 14 cm as centre.

 Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

 
 

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 27

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 28

A regular hexagon is inscribed in a circle. If the area of hexagon is Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles, find the area of the circle. (Use π it = 3.14)

Solution 28

Consider the following figure:

 

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles 

 

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 29

Four equal circles, each of radius 5 cm, touch each other as shown in Fig. Find the area included between them (Take π = 3.14)

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 29

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 30

ABCDEF is a regular hexagon with centre O (Fig.,). If the area of triangle OAB is 9 cm2, find the area of: (i) the hexagon and (ii) the circle in which the hexagon is inscribed.

 

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles 

Solution 30

(i)

According to the figure in the question, there are 6 triangles.

Area of one triangle is 9 cm2.

Area of hexagon = 6 × 9 = 54 cm2

 

(ii)

Area of the equilateral triangle = 9 cm2

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Area of the circle in which the hexagon is inscribed

= Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

= Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

= Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

= 65.26 cm2

 

NOTE: Answer not matching with back answer.

Question 31

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 31

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 32

A child makes a poster on a chart paper drawing a square ABCD of side 14 cm. She draws four circles with centre A, B, C and D in which she suggests different ways to save energy. The circles are drawn in such a way that each circle touches externally two of the three remaining circles. In the shaded region she write a message 'Save Energy'. Find the perimeter and area of the shaded region. (Use π = 22/7)

 

 

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles 

Solution 32

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 33

 

The diameter of a coin is 1 cm. If four such coins be placed on a table so that the rim of each touches that of the other two, find the area of the shaded region (Take π = 3.1416)

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles
Solution 33

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 34

Two circular pieces of equal radii and maximum area, touching each other are cut out from a rectangular card board of dimensions 14 cm × 7 cm. find the area of the remaining card board. (π = 22/7)

Solution 34


Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles




Question 35

AB and CD are two diameters of a circle perpendicular to each other and OD is the diameter of the smaller circle. If OA = 7 cm, find the area of the shaded region.

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 35

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 36

PSR, RTQ and PAQ are three semi-circles of diameters 10 cm, 3 cm and 7 cm respectively. Find the perimeter of the shaded region.

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

 

 

Solution 36

 

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles




Question 37

Two circles with centres A and B touch each other at the point C. If AC = 8 cm and AB = 3 cm, find the area of the shaded region.

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles
Solution 37

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 38

ABCD is a square of side 2a. Find the ratio between

(i) the circumferences

(ii) the areas of the incircle and the circum-circle of the square.

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles
Solution 38

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 39

There are three semicircles, A, B and C having diameter 3 cm each, and another semicircle E having a circle D with diameter 4.5 cm are shown. Calculate:

(i) the area of the shaded region

(ii) the cost of painting the shaded region at the rate of 25 paise per cm2, to the nearest rupee.

 

 

 

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles
Solution 39

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 40

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles
Solution 40

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 41

O is the centre of a circular arc and AOB is a straight line. Find the perimeter and the area of the shaded region correct to one decimal place. (Take π = 3.142)

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles
Solution 41

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 42

The boundary of the shaded region consists of four semi-circular arcs, the smallest two being equal. If the diameter of the largest is 14 cm and of the smallest is 3.5 cm, find (i) the length of the boundary   (ii) the area of the shaded region.

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles
Solution 42

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 43

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Ab = 36 cm and M is mid-point of AB. Semi-circles are drawn on AB, AM and MB as diameters. A circle with centre C touches all the three circles. Find the area of the shaded region.

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 43

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 44

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles
Solution 44

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 45

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles
Solution 45

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 46

Shows a kite in which BCD is the shape of a quadrant of a circle of radius 42 cm. ABCD is a square and Δ CEF is an isosceles right angled triangle whose equal sides are 6 cm long. Find the area of the shaded region.


Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 46

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 47

ABCD is a trapezium of area 24.5 cm2. In it, AD BC, DAB = 90°, AD = 10 cm and BC = 4 cm. If ABE is a quadrant of a circle, find the area of the shaded region.

(π = 22/7)

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 47

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 48

ABCD is a trapezium with AB DC, AB = 18 cm, DC = 32 cm and the distance between AB and DC is 14 cm. Circles of equal radii 7 cm with centres A, B, C and D have been drawn. Then, find the area of the shaded region of the figure. (π = 22/7)

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 48

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Since the data given in the question seems incomplete and inconsistent with the figure, we make the following assumptions to solve it:

1. ABCD a symmetric trapezium with AD = BC

2. AD = BC = 14 cm (the distance between AB and CD is not 14 cm)

Draw perpendiculars to CD from A and B to divide the trapezium into one rectangle and two congruent right angled triangles.

The base of the right angled triangle=(CD - AB) ÷ 2

=(32 - 18) ÷ 2=7 cm

cosD = base ÷ hypotenuse = 7 ÷ 14 =1/2

mD = 60° 

Hence, mA = 120° 


Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

*Answer is not matching with textbook answer.

Question 49

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

 

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 49

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 50

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles
Solution 50

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 51

Sides of a triangular field are 15 m, 16 m and 17 m. With the three corners of the field a cow, a buffalo and a horse are tied separately with ropes of length 7 m each to graze in the field. Find the area of the field which cannot be grazed by three animals.

Solution 51

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

 

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Question 52

In the given Fig., the side of square is 28 cm, and radius of each circle is half of the length of the side of the square where O and O' are centres of the circles. Find the area of shaded region.

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles 

Solution 52

According to the question,

Side of a square is 28 cm.

Radius of a circle is 14 cm.

Required area = Area of the square + Area of the two circles - Area of two quadrants …(i)

Area of the square = 282 = 784 cm2

Area of the two circles = 2πr2

= Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

= 1232 cm2

Area of two quadrants = Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

= Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

= 308 cm2

Required area = 784 + 1232 - 308 = 1708 cm2

 

NOTE: Answer not matching with back answer.

Question 53

In a hospital used water is collected in a cylindrical tank of diameter 2 m and height 5 m. After recycling, this water is used to irrigate a park of hospital whose length is 25 m and breadth is 20 m. If tank is filled completely then what will be the height of standing water used for irrigating the park?

Solution 53

According to the question,

For a cylindrical tank

d = 2 m, r = 1 m, h = 5 m

Volume of the tank = πr2h

  = Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

 = Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

After recycling, this water is used irrigate a park of a hospital with length 25 m and breadth 20 m.

If the tank is filled completely, then

Volume of cuboidal park = Volume of tank

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

h = 0.0314 m = 3.14 cm = p cm

Chapter 15 - Areas Related to Circles Exercise 15.68

Question 1

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 1

Correct Option (b)

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Chapter 15 - Areas Related to Circles Exercise 15.69

Question 1

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 1

Correct option - (c)

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles