watch 01:36
We're Getting Mutants in the MCU - The Loop
Do you like this video?
Play Sound
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

Figure 2. Half a parabola
Consider half a parabola where the interval of
is :where
is constant.At
, we have .At
, we have .Solving for the constant yields
; thus,- .
Use the disk method to calculate the volume:
When compared with the volume the cylinder
, the volume of the paraboloid is half the volume of the cylinder.