## Book: RS Aggarwal - Mathematics

### Chapter: 18. Area of Circle, Sector and Segment

#### Subject: Maths - Class 10th

##### Q. No. 3 of Exercise 18B

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##### The circumference of a circle exceeds its diameter by 45 cm. Find the circumference of the circle.

Given, the circumference of a circle exceeds its diameter by 45 cm.

Circumference of circle = Diameter of circle + 45

Let ‘d’ = diameter of the circle

Circumference = d + 45 eqn1

And we know, Circumference of a circle = 2πr eqn2

Where r = radius of circle

Also, we know that the radius of the circle is half of its diameter.

Put value of circumference in equation 1 from equation 2

2πr = d + 45 eqn4

Put value of r in equation 4 from equation 3

πd = d + 45

πd – d = 45

(π – 1)d = 45 (taking d common from L.H.S)

On rearranging, we get

d = 21 cm

Therefore, the diameter of the circle is 21 cm.

Thus, the radius of the circle

r = 10.5 cm

Now put the value of r in equation 2, we get

= 66 cm

The circumference of the circle is 66 cm.

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