Question:
A well with 14 m diameter is dug 8 m deep. The earth taken out of it has been evenly spread all around it to a width of 21 m to form an embankment. Find the height of the embankment.
Solution:
Let, r be the radius of well
h be the height of well
here, h = 8 m
2r = 14
⟹ r = 14/2
= 7m
Volume of well $=r^{2} * h$
= 22/7 * 7 * 7 * 8
= 22 * 56
$=1232 \mathrm{~m}^{3}$
Let, re be the radius of embankment
he be the height of embankment
Volume of well = Volume of embankment
$1232 \mathrm{~m}^{3}=\pi * \mathrm{r}_{\mathrm{e}} * \mathrm{~h}_{\mathrm{e}}$
$1232=22 / 7 *\left(28^{2}-7^{2}\right) * h_{e}$
$\mathrm{h}_{\mathrm{e}}=\frac{1232 * 7}{22(784-49)}$
$\mathrm{h}_{\mathrm{e}}=\frac{1232 * 7}{22 * 735}$
he = 0.533 m