Question

A road which is 7 m wide surrounds a circular park whose circumference is 88 m. Find the area of the road.

Answer 1

Given,

Circumference of a circular park = 88 m

Width of a road = 7 m

Since, circumference = 2πr

∴ 88 = 2πr

⇒ `r = 88/(2π)`

= `(88 xx 7)/(2 xx 22)`

= 2 × 7

= 14 m

∴ Inner radius of the park (r) = 14 m

Outer radius of the park including the road (R)

= width + r

= 7 + 14

= 21 m

Area of the road = π(R² – r²)

= π(R + r)(R – r)   ...[∵ a² – b² = (a + b)(a – b)]

= `22/7 (21 + 14)(21 - 14)`

= `22/7 xx 35 xx 7`

= 770 m²

Hence, the area of the road is 770 m².