Problem
Use integration to derive the volume of a paraboloid of radius
and height . Compare the volume of the paraboloid to the volume of the cylinder with equal base and height.Solution
Consider half a parabola where the interval of
is .At
,- .
At
,- .
Therefore,
and
- .
Use the disk method to calculate the volume.
Comparing with the volume the cylinder,
, the volume of the paraboloid is half the volume of the cylinder.
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