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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 embankmentVolume 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 =31.5πm3Volume 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)2−πh(1.5)2 =πh(30.25−2.25) =πh(28) =28πhm3⇒ Volume of embankment =28πhm3Now, volume of well = volume of embankment ⇒31.5π=28πh∴h=31.528=1.125m.Hence, the answer is 1.125m.

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