Question

A circular park is surrounded by a road 21 m wide. If the radius of the park is 105 m, find the area of the road.

Answer 1

Circular road and park are concentric circles.

Radius of the park = r₁ = 105 m

Width of road = 21 m

Radius of circular road and park = r₂​

= 105 m + 21 m

= 126 m

So, Area of road = Area of park and road – Area of park

= `π"r"_2^2 - π"r"_1^2`

= `π["r"_2^2 - "r"_1^2]`

= `22/7 [(126)^2 - (105)^2]`

= `22/7 [126 - 105][126 + 105]`

= `22/7 xx 21 xx 231`

= 22 × 3 × 231

= 66 × 231

= 15246 cm²

∴ Area of road = 15246 cm²