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Question

A well of diameter 3 m is dug 14 m deep. The earth taken out of it has been spread evenly all around it to a width of 4 m to form an embankment. Find the height of the embankment.


Solution

Height of the well = 14 m
Diameter of the well = 3 m
So, Radius of the well = 32 m
Volume of the earth taken out of the well =πr2h=227×(32)2×14=99 m3


Outer radius of the embankment = R = (32 + 4)m = 112  m
Area of embankment = outer area - inner area

=πR2πr2

=227[(112)2(32)2]

=227[121494]

=227×1124=88 m2
Height of the embankment =VolumeArea=9988=1.125 m
Height of the embankment = 1.125 m

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