Question

A circular pond is of diameter 17.5 m. It is surrounded by a 2 m wide path. Find the cost of constructing the path at the rate of Rs 25 per square metre (Use π = 3.14) [CBSE 2014]

Answer 1

Let the radius of outer and inner circles be r₁ and r₂ respectively.
Area of the path = $\mathrm{\pi }{r_1}^2-\mathrm{\pi }{r_2}^2$
$$\begin{gathered} =3.14\left[{\left(\frac{17.5}{2}+2\right)}^2-{\left(\frac{17.5}{2}\right)}^2\right] \\ =3.14\left[{\left(10.75\right)}^2-{\left(8.75\right)}^2\right] \\ =3.14\times 39 \\ =122.46{\mathrm{cm}}^2 \end{gathered}$$
Now, Cost of constructing the path = Area of the path ⨯ Rate
= 122.46 ⨯ 25
= Rs 3061.5

Hence, the cost of constructing the path is Rs 3061.5