# Class 10 NCERT Solutions 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.

## Areas Related to Circles Exercise Ex. 12.1

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Let the radius of the circle be *r*

Circumference of circle = 2*r*

Area of circle = *r*^{2}

Given that circumference and area of the circle are equal.

So, 2*r* = *r*^{2}

2 = *r*

Hence, the radius of the circle will be 2 units

## Areas Related to Circles Exercise Ex. 12.2

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### Solution 6

Radius (r) of the circle = 15

Area of sector OPRQ =

=

=

= 117.75 cm^{2}

In ∆OPQ

.... (Since OP = OQ)

\

Area of ∆OPQ =

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

= 117.75 – 97.3125

= 20.4375 cm^{2}

Area of major segment PSQ

= Area of circle – Area of segment PRQ

= 15^{2}p – 20.4375

= 3.14 × 225 – 20.4375

= 686.0625 cm^{2}

### Solution 7

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

SV = VT

In ∆OVS

OV = 6

ST = 2SV =

Area of ∆OST =

=

=

= 36 × 1.73

= 62.28

Area of sector OSUT =

= 150.72

Area of segment SUT = Area of sector OSUT

= 150.72 – 62.28

= 88.44 cm^{2}

### Solution 8

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

=

=

= 19.63 m^{2}

ii. Area that can be grazed by the horse when the length of rope is 10 m long =

=

= 78.5

Change in grazing area = 78.5 – 19.63 = 58.87 cm^{2}

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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.

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## Areas Related to Circles Exercise Ex. 12.3

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