Question

Question 14
A circular park is surrounded by a road 21 m wide. If the radius of the park is 105 m, then find the area of the road.

Answer 1

[$\because$ Area of the circle $=\pi r^2$]

Given that a circular park is surrounded by a road

Width of the road = 21 m

Radius of the park $\left(r_1\right)=105m$

$\therefore$ Radius of whole circular portion ( Park + road)

$r_e=105+21=126m$

Now, area of road = Area of whole circular portion - Area of circular park

$=\pi r_e^2-\pi r_1^2[\therefore Areaofcircle=\pi r^2]$

$=\pi (r_e^2-r_1^2)$

$=\pi \left\{\right({126}^2-\left(105{)}^2\right)\}$

$=\frac{22}{7}\times (126+105)(126-105)$

$=\frac{22}{7}\times 231\times 21$

$[\because (a^2-b^2)=(a-b\left)\right(a+b\left)\right]$

$=66\times 231$

$=15246c{m}^2$

Hence, the required area of the road is $=15246c{m}^2$