Question

A road which is 7 m wide surrounds a circular park whose circumference is 352 m. Find the surface area of the road.

Answer 1

Given: A road 7 m wide surrounds a circular park whose circumference = 352 m.

Step-wise calculation:

1. Let r = radius of the park.

Circumference = 2πr

= 352

r = `352/(2π)` 

= `352/(2 xx 22/7)` 

= `(352 xx 7)/44` 

= 56 m

2. Outer radius

R = r + 7 

= 56 + 7 

= 63 m

3. Area of the road

= π(R² – r²) 

= π(63² – 56²) 

= π(63 – 56)(63 + 56)

= π × 7 × 119

= 7 × 119 × π

= 833π m²

Using π = `22/7` gives area

= `22/7 xx 7 xx 119` 

= 22 × 119

= 2618 m²

Surface area of the road = 2618 m².