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

Given:

A road which is 7 m wide surrounds a circular park whose circumference is 352 m.

To do:

We have to find the area of the road.

Solution:

Let $R$ be the radius of the circular park.

Width of the road $= 7\ m$.

Circumference of the park $= 352\ m$.

This implies,

$2\pi R = 352$

$2 \times \frac{22}{7} R=352$

$R=352\times\frac{7}{44}$

$R=8\times7$

$R=56\ m$

This implies,

Outer radius $=R+7=7+56=63\ m$

Therefore,

Area of the road $=\pi (R+7)^2- \pi R^2$

$=\frac{22}{7}(63^2-56^2)$

$=\frac{22}{7}\times(3969-3136)$

$=\frac{22}{7}\times833$

$=22\times119$

$=2618\ m^2$

The area of the road is $2618\ m^2$.

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Updated on: 10-Oct-2022

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