A circular park is surrounded by a road 21 m wide. If the radius of theĀ park is 105 m, then find the area of the road.
Given that, a circuiar park is surrounded by a road.
Width of the road $=21 \mathrm{~m}$
Radius of the park $(r)=105 \mathrm{~m}$
$\therefore$ Radius of whole circular portion (park + road),
Now, area of road = Area of whole circular portion
- Area of circular park
$=\pi r_{8}^{2}-\pi r_{i}^{2} \quad\left[\therefore\right.$ area of circle $\left.=\pi r^{2}\right]$
$=\pi\left(t_{e}^{2}-r_{i}^{2}\right)$
$=\pi\left\{\left(126^{2}-(105)^{2}\right\}\right.$
$=\frac{22}{7} \times(126+105)(126-105)$
$=\frac{22}{7} \times 231 \times 21 \quad\left[\because\left(a^{2}-b^{2}\right)=(a-b)(a+b)\right]$
$=66 \times 231$
$=15246 \mathrm{~cm}^{2}$
Hence, the required area of the road is $15246 \mathrm{~cm}^{2}$.