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:

Diameter of the well = d m = 14 m

Height of the well = h m = 8 m

Radius of the well = r m = 7 m

Volume of the well = πrh = π(7 m)2(8 m) = 1232 m3

Volume of the well = Volume of the embankment

An embankment is a hollow cylinder with thickness. Its inner radius would be equal to the radius of the well, i.e. $r=7 \mathrm{~m}$, and its outer radius is $R=$ $7+21=28 \mathrm{~m}$.

Volume of the embankment $=\pi h\left(R^{2}-r^{2}\right)$

To find the height (h), we use the fact that the volume of the embankment is equal to the volume of the well.

1232= πh ((28)2-(7)2)

$h=\frac{1232}{\frac{22}{7} \times\left[(28)^{2}-(7)^{2}\right]}=0.533 \mathrm{~m}$

Hence, the height of the embankment is 0.533 m or 53.3 cm.