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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 in the shape of a circular ring of width 4 m to form an embankment. Find the height of the embankment. [3 MARKS]

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Solution

Concept: 1 Mark
Application: 2 Marks

Diameter of the well = d = 3 m

Radius of well =r=d2=1.5m

Height of the well = h= 14 m


Volume of earth dug out = volume of well
=π.r2.h=π×1.5×1.5×14=31.5π m3

Let the height of the embankment be h1 m

Volume of embankment
=π.((r2)2(r1)2)).h1 (r2=5.5 ,r1=1.5)
=π.((5.5)2(1.5)2)).h1=π.(30.252.25).h1=28π.h1 m3

According to the given condition , we have:

Volume of Earth Dug out = volume of embankment

31.5π=28π.h1

h1=31.528=1.125m


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