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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=1232227×[(28)2-(7)2]=0.533 m

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

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