Question

The radius of a circular garden is 100 m. There is a road 10 m wide, running all around it. Find the area of the road and the cost of levelling
it at Rs 20 per m². [Use π = 3.14] [CBSE 2011]

Answer 1

Area of the road = Area of outer circle − Area of inner circle
$$\begin{gathered} =\mathrm{\pi }{R}^2-\mathrm{\pi }{r}^2 \\ =\mathrm{\pi }\left[{\left(110\right)}^2-{\left(100\right)}^2\right] \\ =3.14\times 2100 \\ =6594{\mathrm{m}}^2 \end{gathered}$$
Cost of levelling the road = Area of the road ⨯ Rate
= 6594 ⨯ 20
= Rs 131880