NCERT Solutions for Class 10 Maths Chapter 12 - Areas Related to Circles

Brush up your knowledge of circles with NCERT Solutions for CBSE Class 10 Mathematics Chapter 12 Areas Related to Circles. Learn to calculate the number of revolutions made by the wheel of a car based on the dimensions of the wheel. Practise the method to work out the area of a sector in a given Maths problem related to circles.

Also, practise the ways to calculate the area of a semicircle or the area of a specific design with the step-wise answers in our textbook solutions. To boost your Maths skills for board exam preparation, utilise TopperLearning’s CBSE Class 10 Maths videos, question papers, practice tests and more.

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Chapter 12 - Areas Related to Circles Exercise Ex. 12.1

Solution 1

Ncert Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 2

Ncert Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 3


Ncert Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Ncert Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles
Solution 4

Ncert Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 5

Let the radius of the circle be r

Circumference of circle = 2Ncert Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circlesr

Area of circle = Ncert Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circlesr2

Given that circumference and area of the circle are equal.

So, 2Ncert Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circlesr = Ncert Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circlesr2

2 = r

Hence, the radius of the circle will be 2 units

Chapter 12 - Areas Related to Circles Exercise Ex. 12.2

Solution 1

Ncert Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 2

Ncert Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 3

Ncert Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 4

Ncert Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 5

Ncert Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Ncert Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles
Ncert Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles
Solution 6


Ncert Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

 

Radius (r) of the circle = 15

Area of sector OPRQ =Ncert Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

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

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

= 117.75 cm2

In ∆OPQ

Ncert Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles.... (Since OP = OQ)
Ncert Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles
\Ncert Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Ncert Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

∆OPQ is an equilateral triangle.

Area of ∆OPQ =Ncert Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Area of segment PRQ = Area of sector OPRQ –Area of ∆OPQ

                                = 117.75 – 97.3125

                                = 20.4375 cm2

Area of major segment PSQ

= Area of circle – Area of segment PRQ

= 152p20.4375

= 3.14 × 225 – 20.4375

= 686.0625 cm2
Solution 7

Ncert Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

 

Draw a perpendicular OV on chord ST. It will bisect the chord ST.

SV = VT

In ∆OVS

Ncert Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Ncert Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

OV = 6

Ncert Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Ncert Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles 

Ncert Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

ST = 2SV = Ncert Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Area of ∆OST = Ncert Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Ncert Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Ncert Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

= 36 × 1.73

= 62.28

Area of sector OSUT = Ncert Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

= 150.72

Area of segment SUT = Area of sector OSUT

                                = 150.72 – 62.28

                                = 88.44 cm2

Solution 8

Ncert Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

The horse can graze a sector of 90° in a circle of 5 m radius.

i.     So area that can be grazed by horse = area of sector OACB

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

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

       = 19.63 m2

ii.    Area that can be grazed by the horse when the length of rope is 10 m long = Ncert Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

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

       = 78.5

Change in grazing area = 78.5 – 19.63 = 58.87 cm2

Solution 9

Ncert Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 10

Ncert Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 11

Ncert Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

The figure shows that each blade of the wiper will sweep an area of a sector of 115° in a circle of 25 cm radius.

Ncert Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 12

Ncert Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 13

Ncert Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Ncert Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 14

Ncert Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Chapter 12 - Areas Related to Circles Exercise Ex. 12.3

Solution 1

Ncert Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Ncert Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 2

Ncert Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles
Ncert Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 3

Ncert Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Ncert Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 4

Ncert Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Ncert Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 5

Ncert Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Ncert Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 6

Ncert Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Ncert Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles
Ncert Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 7

Ncert Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Ncert Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 8

Ncert Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Ncert Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 9

Ncert Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Ncert Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 10

Ncert Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Ncert Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 11

Ncert Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 12

Ncert Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Ncert Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 13


Ncert Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 14

Ncert Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Ncert Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 15

Ncert Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Ncert Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Solution 16

Ncert Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles

Ncert Solutions Cbse Class 10 Mathematics Chapter - Areas Related To Circles