Question

In a village, a well with 10 m inside diameter, is dug 14 m deep. Earth taken out of it is spread all around to a width 5 m to form an embankment. Find the height of the embankment. What value of the villagers is reflected here? [CBSE 2014]

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{have}, \\ \mathrm{Radius}\mathrm{of}\mathrm{well},R=\frac{10}{2}=5\mathrm{m}, \\ \mathrm{Depth}\mathrm{of}\mathrm{the}\mathrm{well},H=14\mathrm{m}\mathrm{and} \\ \mathrm{Width}\mathrm{of}\mathrm{the}\mathrm{embankment}=5\mathrm{m}, \\ \mathrm{Also},\mathrm{the}\mathrm{outer}\mathrm{radius}\mathrm{of}\mathrm{the}\mathrm{embankment},r=R+5=5+5=10\mathrm{m} \\ \mathrm{And},\mathrm{the}\mathrm{inner}\mathrm{radius}\mathrm{of}\mathrm{the}\mathrm{embankment}=R=5\mathrm{m} \\ \mathrm{Let}\mathrm{the}\mathrm{height}\mathrm{of}\mathrm{the}\mathrm{embankment}\mathrm{be}h. \\ \mathrm{Now}, \\ \mathrm{Volume}\mathrm{of}\mathrm{the}\mathrm{embankment}=\mathrm{Volume}\mathrm{of}\mathrm{the}\mathrm{earth}\mathrm{taken}\mathrm{out} \\ \Rightarrow \mathrm{Volume}\mathrm{of}\mathrm{the}\mathrm{embankment}=\mathrm{Volume}\mathrm{of}\mathrm{the}\mathrm{well} \\ \Rightarrow \left(\mathrm{\pi }{r}^2-\mathrm{\pi }{R}^2\right)h=\mathrm{\pi }{R}^{2}H \\ \Rightarrow \mathrm{\pi }\left(r^2-R^2\right)h=\mathrm{\pi }{R}^{2}H \\ \Rightarrow \left(r^2-R^2\right)h=R^{2}H \\ \Rightarrow \left({10}^2-5^2\right)h=5\times 5\times 14 \\ \Rightarrow \left(100-25\right)h=25\times 14 \\ \Rightarrow 75h=25\times 14 \\ \Rightarrow h=\frac{25\times 14}{75} \\ \therefore h=\frac{14}{3}\mathrm{m} \end{gathered}$$

So, the height of the embankment is $\frac{14}{3}$ m.

Value: We must lanour hard to make maximum use of the available resources.

Disclaimer: The answer provided in the textbook is incorrect. It has been corrected above.