## Book: RS Aggarwal - Mathematics

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

#### Subject: Maths - Class 10th

##### Q. No. 9 of Exercise 18B

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9
##### A path of 8 m width runs around the outside of a circular park whose radius is 17 m. Find the area of the path.

Given radius of circular park = R = 17 m

Width of the circular path outside the park = d = 8 m

Therefore, the radius of the outer circle = R’ = R + d

Outer radius = R’ = 17 + 8

R’ = 25 m

Area of inner circle = πR2 and,

Area of outer circle = πR’2

Area of path = Area of outer circle – Area of inner circle

= πR’2 – πR2 (put values of R’ & R)

= π(252) – π(172)

= π(252 – 172) (taking π common from R.H.S)

= π(625 – 289)

(put π = 22/7)

= 7392/7

= 1056 m2

The area of the path is 1056 m2.

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