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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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