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.

Explanation

Given that, a circular park is surrounded by a road.
Width of the road = 21 m
Radius of the park `(r_(i)) = 105 m`
`:.` 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
= `pir_(e)^(2) - pir_(i)^(2)`
= `pi(r_(e)^(2) - r_(i)^(2))`
= `pi{(126)^(2)- (105)^(2)}`
= `(22)/(7)xx(126+105)(126 - 105)`
= `(22)/(7)xx231 xx21` [`because(a^(2) -b^(2)) = (a - b)(a+b)`]
=`66xx231`
= `15246 cm^(2)`
Hence, the required area of the road is `15246 cm^(2)` .