A road which is 7 m wide surrounds a circular park whose circumference is 352 m. Find the area of the road. [Take π = 22/7.]
fig.17
Let the radius of the circular park be r meters.
Given –
Circumference of circular park = 352 m
⇒ 2 × π × r = 352
⇒ 2 × (22/7) × r = 352
⇒ r = (7/44) × 352
∴ r = 7 × 8 = 56 m
⇒ outer radius = 56 + 7 = 63 m
∴ Area of the road = π(632 – 562)
= (22/7)(63 + 56)(63 – 56)
= (22/7)(119)(7)
= 22 × 119
= 2618 m2