Question

A 7 m broad pathway goes around a circular park with a circumference of 352 m. Find the area of road.

Answer 1

The circumference of the circular park = 352 m.

Let r be the radius of the circular park.

Then, 2πr = 352

`2 xx 22/7 xx r` = 352

r = `(352 xx 7)/(2 xx 22)` = 56 m

Area of circular park = πr²

= `22/7 xx (56)^2`

= `22/7 xx 56 xx 56`

= 22 × 8 × 56

= 9856 m²

Now, the circular park's radius with road,

R = 56 + 7 = 63 m

∴ Circular park area with a road

= πR²

= `22/7 xx (63)^2`

= `22/7 xx 63 xx 63`

= 22 × 9 × 63

= 12474 m²

So, Area of road = Area of circular park with road – Area of circular park

= 12474 – 9856

= 2618 m²

Hence, the area of road is 2618 m².