The region R and the solid formed by its revolution is shown
in the figure above. Consider a strip of length x and width dy at a distance y
from the origin in the Region R. When it
is revolved about y axis, the volume of the circular disc formed will be πx2dy.
The volume of the container formed will be 
. Substituting x= y2+1 (obtained by squaring the
equation of the curve and solving for x) we will have Volume=
= 
=
=
Now consider the container to be filled by olive oil. The mass of an elementary circular element of the olive oil at height y from its base, radius and width dy will be 915 πx2dy kg. The weight of the element will be 9.8 (915) πx2dy Kg M/Sec2 or N
Work done in lifting this element to the top(Moving it up by
a distance 2-y) will be 9.8 (915) πx2dy (2-y) Nm
. Hence Total work
done in pumping the oil of the container will be 
=8967π
=8967π
Nm
=191463.384Nm
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