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Question

A well with 14m diameter is dug 8m deep. The earth taken out of it has been evenly spread all around it to a width of 21m to form an embankment. Find the height of the embankment.

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Solution

Diameter of the well =14m


Radius(r) =142=7m
Depth of well (h) =8m
Volume of earth dug out = πr2h
=227×7×7×8m3=1232m3
Width of embankment =21m
outer radius =21+7=28m
Area of embankment = π(R2r2)
=227(28272)m2=227(28+7)(287)m2=227×35×21m2=2310m2
Let h be the height of embankment, then
Volume of embankment = 2310×h.
2310h=1232
h=12322310=0.53m=53cm
Hence height of embankment= 53cm

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