A well with 14 m diameter is dug 8 m deep.
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

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