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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 circular ring of width 4m to form an embankment. Find the height of the embankment.

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Solution

Both well and embankment are in the form of cylinder. Let well be cylinder A and embankment be cylinder B.
mud of well is distributed in embankment
Volume of well = Volume of embankment
Volume of well -
For A, r=32m=1.5m,height=14m
Volume of cylinder A =πr2h
=π×(1.5)2×14
=31.5πm3
Volume of well = Volume of cylinder A =31.5πm3
Volume of embankment -
For cylinder B,
Cylinder B is a hollow cylinder with inner radius r1=32=1.5m
External radius r2= internal radius + width
=1.5+4
=5.5m
Volume of cylinder with internal radius =πr21h
=πh(1.5)2
Volume of cylinder with external radius =πr22h
=πh(5.5)2
Volume of cylinder B =πh(5.5)2πh(1.5)2
=πh(30.252.25)
=πh(28)
=28πhm3
Volume of embankment =28πhm3
Now, volume of well = volume of embankment
31.5π=28πh
h=31.528=1.125m.
Hence, the answer is 1.125m.



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