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.

Answer 1

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 = πr² h = 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 m, and its outer radius is R = 7 + 21 = 28 m.

Volume of the embankment = πh(R²-r²)

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)
$h=\frac{1232}{{\displaystyle \frac{22}{7}}\times \left[\right(28{)}^2-\left(7{)}^2\right]}=0.533\mathrm{m}$
Hence, the height of the embankment is 0.533 m or 53.3 cm.