The volume of a solid of revolution can be calculated by making use of some methods of integral calculus. For that you will need the exact equation of the the surface that limits the solid. Nothing you can do on a calculator.
However for the spheroids there exit formulas you can use on a calculator.
If a, b, c are the lengths of the semiaxes (
length of semiaxis=half the length of the axis)
V=(4/3)PI*a*b*c
An oblate spheroid is the solid of revolution formed by the rotation of an ellipse about its minor axis (here an image of the cross section from Wikipedia).
V=(4/3)PI*(a^2)*b
A prolate spheroid is the solid of revolution formed by the rotation of an ellipse about its major axis
V=(4/3)PI*a*(b^2)
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