Question

A circular park is surrounded by a road $21m$ wide. If the radius of the park is $105m$, find the area of the road.

• A. $13860m^2$
• B. $30492m^2$
• C. $7623m^2$
• D. $15246m^2$

Answer 1

The correct option is D $15246m^2$

$O$ is the centre of a circular park of radius $OA=105m$ with a concentric surrounding circular road of width $AB=21m$

To find the area of the road, first we need to find area of the park and then subtract the area of park from total area including road.

Let's find area of a park.

Park forms a circle with radius$\left(r\right)=105m$

$\therefore$ Area of the park $=\pi r^2=\pi (105{)}^2$

The outer circle represents total area which includes park and road with radius$\left(R\right)=105+21=126$

$\therefore$ Total area $=\pi R^2=\pi (126{)}^2$

Thus, area of the road $=$ Total area $-$ Area of park

$=\pi (126{)}^2-\pi (105{)}^2=\pi ({126}^2-{105}^2)=4851\pi =15246m^2$

Hence, area of road $=15246m^2$