Question

A circular pond is of diameter 17.5 m . It is surrounded by a 2m wide path . Find the cost of constructing the path at the rate of ₹25 per square metre $\left(Use\mathrm{\pi }=\frac{22}{7}\right)$

Answer 1

Diameter, d = 17.5 m
Radius, r = $\frac{17.5}{2}\mathrm{m}$
Radius of the pond with the 2 m wide path = $2+\frac{17.5}{2}$ m
Area of the circular path = Area of the pond with the path − area of the pond
$$\begin{gathered} =\mathrm{\pi }{\left(2+\frac{17.5}{2}\right)}^2-\mathrm{\pi }{\left(\frac{17.5}{2}\right)}^2 \\ =122.57{\mathrm{m}}^2 \end{gathered}$$
Cost of constructing the path = $25\times 122.57=\mathrm{Rs}3064.2$