Question

A well with 10 m inside diameter is dug 14 m deep. Earth taken out of it is spread all around to a width of 5 m to form an embankment. Find the height of the embankment.

Answer 1

Let h m be the height of the embankment.
Internal radius of the well, r =5 m
$$\begin{gathered} \mathrm{Volume}\mathrm{of}\mathrm{earth}\mathrm{dug}\mathrm{out}=\mathrm{\pi }{r}^{\mathit{2}}h \\ =\frac{22}{7}\times 5\times 5\times 14 \\ =22\times 5 \\ =1100{\mathrm{m}}^3 \end{gathered}$$

Here, external radii = 10 m; internal radii = 5 m

Now, area of the embankment = $\mathrm{\pi }\left({10}^2-5^2\right)=\frac{22}{7}\times 75=\frac{1650}{7}{\mathrm{m}}^2$

∴ Height of the embankment = $\frac{\mathrm{volume}\mathrm{of}\mathrm{earth}\mathrm{dug}\mathrm{out}}{\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{embankment}}=\frac{1100}{{\displaystyle \frac{1650}{7}}}=4.67\mathrm{m}$