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

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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

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