Question

A circular pond is 17.5 m in diameter. It is surrounded by a 2m wide path, Find the cost of constructing the path at the rate of ₹ 25 per m² .

Answer 1

Diameter of the pond = 17.5 m
Radius of the pond = 8.75 m
Radius of the pond with the path = 8.75 + 2 = 10.75 m
Area of the path = Area of the pond along with the path − area of the pond
$$\begin{gathered} \mathrm{Area}\mathrm{of}\mathrm{the}\mathrm{path}=\mathrm{\pi }\left[{\mathrm{R}}^2-{\mathrm{r}}^2\right] \\ =\mathrm{\pi }\left[{\left(10.75\right)}^2-{\left(8.75\right)}^2\right] \\ =\mathrm{\pi }\left[\left(2\right)\left(19.5\right)\right] \\ =122.46{\mathrm{m}}^2 \end{gathered}$$
Cost of constructing the path = $25\times 122.46=\mathrm{Rs}3061.5$