Question

The inner circumference of a circular track is 440 m, and the track is 14 m wide. Calculate the cost of levelling the track at 25 paise/m². Also, find the cost of fencing the outer boundary of the track at Rs 5 per metre.

Answer 1

Let the radius of the inner circle be r m.
Now,
Inner circumference = 440 m
$\Rightarrow 2\mathrm{\pi r}=440$
$$\begin{gathered} \Rightarrow 2\times \frac{22}{7}\times r=440 \\ \Rightarrow r=\frac{440\times 7}{44} \\ \Rightarrow r=70 \end{gathered}$$

We know that the track is 14 m wide.
∴ Outer radius (R) = (70 + 14) = 84 m

$$\begin{gathered} \mathrm{Area}\mathrm{of}\mathrm{the}\mathrm{track}=\mathrm{\pi }({\mathrm{R}}^2-r^2) \\ =\mathrm{\pi }\left({84}^2-{70}^2\right) \\ =\frac{22}{7}\times \left(7056-4900\right) \\ =6776\hspace{0.17em}{\mathrm{m}}^2 \end{gathered}$$

Cost of levelling at 25 paise per square metre $=6676\times 25=169400\mathrm{paise}$
Or,
$\mathrm{Rs}\frac{169400}{100}=\mathrm{Rs}1694$
​
∴ Outer circumference = $2\mathrm{\pi R}$
$$\begin{gathered} =2\times \frac{22}{7}\times 84 \\ =528\mathrm{m} \end{gathered}$$

Rate of fencing = 5 per metre
∴ Total cost of fencing $=528\times 5=\mathrm{Rs}2640$