Question

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

Answer 1

$\Rightarrow$ Circumference of circular park $=352$

$\therefore$ $2\pi r=352$

$\Rightarrow$ $2\times \frac{22}{7}\times r=325$

$\Rightarrow$ $r=\frac{352\times 7}{2\times 22}=56m$

$\therefore$ Radius of circular park $=56m$

$\Rightarrow$ Area of circular park $=\pi r^2$

$\Rightarrow$ Area of circular park $=\frac{22}{7}\times 56\times 56=9856m^2$

$\Rightarrow$ Width of road $=7m$ [given]

$\therefore$ Area of circular park with road $=\pi (Radius+width{)}^2$

$\Rightarrow$ Area of circular park with road $=\frac{22}{7}\times (56+7{)}^2{m}^2$

$\Rightarrow$ Area of circular park with road $=\frac{22}{7}\times 63\times 63=12474m^2$

$\Rightarrow$ Area of road = Area of circular park with road - Area of circula park

$\Rightarrow$ Area of road $=12474m^2-9856m^2=2618m^2$