A well of inner diameter 14 m is dug to a depth of 15m. 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

$$\begin{gathered} \text{ Radius of the well, }\mathrm{r}=7\mathrm{m},\text{ and its depth, }\mathrm{h}=15\mathrm{m} \\ \text{ Volume of the earth dug out }=\left({\mathrm{\pi r}}^2\mathrm{h}\right)\text{ cubic units } \end{gathered}$$   

$=\left(\frac{22}{7}\times 7\times 7\times 15\right){\mathrm{m}}^3=2310{\mathrm{m}}^3$
Width of the embankment = 7m
External radius of the embankment  $=(7+7)\mathrm{m}=14\mathrm{m}$
Internal radius of the embankment  $=7\mathrm{m}\mid$
Area of the embankment $=\mathrm{\pi }\times \left[(14{)}^2-7^2\right]{\mathrm{m}}^2=\left[\frac{22}{7}\times (14+7)\times (14-7)\right]{\mathrm{m}}^2$
$=\left(\frac{22}{7}\times 21\times 7\right)m^2=462m^2$
Volume of the embankment = volume of the earth dug out $=2310{\mathrm{m}}^3$
$\text{ Height of the embankment }=\left(\frac{\text{ Volume of the embankment in m^3 }}{{\text{ areaof theembankment inm }}^2}\right)=\left(\frac{2310}{462}\right)m=5\mathrm{m}$
Hence, the height of the embankment formed = 5 m