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)2−πh(1.5)2
=πh(30.25−2.25)
=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.