Question

A circular pond is $17.5m$ is of diameter. It is surrounded by a $2m$ wide path. Find the cost of constructing the path at the rate of $Rs25per{m}^2$

Answer 1

Let r be the radius of the park$=\frac{17.5}{2}=8.75m$

The circular pond is surrounded by a path of width$2m$

So, Radius of the outer circle $=R=(8.75+2)m=10.75m$

$\text{Area of the road = Area of the outer circular path – Area of the circular pond}$

$$\begin{gathered} =\pi r^2–\pi R^2 \\ =3.14\times {(10.75)}^2–3.14\times {(8.75)}^2 \\ =3.14\times ({(10.75)}^2–{(8.75)}^2) \\ =3.14\times \left(\right(10.75+8.75)\times (10.75–8.75\left)\right) \\ =3.14\times 19.5\times 2 \\ =122.46m^2 \end{gathered}$$

The area of the path is $122.46m^2$

Cost of constructing the path per m² $=Rs25$

∴ cost of constructing $122.46m^2$of the path $=25\times 122.46=Rs3061.50$

Hence, the cost of constructing$122.46m^2$of the path $=Rs3061.50$