Question

A well of inner diameter 14 m is dug to a depth of 12 m. Earth taken out of it has been evenly spread all around it to a width of 7 m to form an embankment. Find the height of the embankment so formed.

Answer 1

Inner diameter = 14 m
i.e., radius = 7 m
Depth = 12 m
​Volume of the earth dug out$={\mathrm{\pi r}}^2\mathrm{h}=\frac{22}{7}\times 7\times 7\times 12=1848{\mathrm{m}}^3$

Width of embankment = 7 m
Now, total radius $=7+7=14m$

$$\begin{gathered} \mathrm{Volume}\mathrm{of}\mathrm{the}\mathrm{embankment}=\mathrm{total}\mathrm{volume}-\mathrm{inner}\mathrm{volume} \\ ={{\mathrm{\pi r}}_{\mathrm{o}}}^2\mathrm{h}-{{\mathrm{\pi r}}_{\mathrm{i}}}^2\mathrm{h}=\mathrm{\pi h}\left({{\mathrm{r}}_{\mathrm{o}}}^2-{{\mathrm{r}}_{\mathrm{i}}}^2\right) \\ =\frac{22}{7}\mathrm{h}\left({14}^2-7^2\right)=\frac{22}{7}\mathrm{h}\left(196-49\right) \\ =\frac{22}{7}\mathrm{h}\times 147=21\times 22\mathrm{h} \\ =462\times \mathrm{h}{\mathrm{m}}^3 \end{gathered}$$

Since volume of embankment = volume of earth dug out, we have:
$1848=462h$
$\Rightarrow h=\frac{1848}{462}=4m$
∴ Height of the embankment = 4 m