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.

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

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