Question

The cost of fencing a circular field at the rate of Rs 25 per metre is Rs 5500. The field is to be ploughed at the rate of 50 paise per m² . Find the cost of ploughing the field. [Take $\mathrm{\pi }=\frac{22}{7}$].

Answer 1

$\mathrm{Circumference}=\frac{\mathrm{Total}\mathrm{cost}\mathrm{of}\mathrm{fencing}}{\mathrm{Rate}\mathrm{of}\mathrm{fencing}}=\frac{5500}{25}=220$
Let the radius of the circle be r.
​Now,
$$\begin{gathered} \mathrm{Circumference}=220 \\ \Rightarrow 2\mathrm{\pi }r=220 \\ \Rightarrow r=35\mathrm{cm} \end{gathered}$$
Now,
Area of field = $\mathrm{\pi }{r}^2=\frac{22}{7}\times {\left(35\right)}^2=3850{\mathrm{cm}}^2$
Cost of ploughing = Rate ⨯ Area of field = 0.5 ⨯ 3850 = Rs 1925
Hence, the cost of ploughing the field is Rs 1925.