Question

Prove that the volume of any parabola is always half the volume of the circumscribed cylinder?

Prove that the volume of any parabola is always half the volume of the circumscribed cylinder.

Answer 1

Compare the two volume equations.

Explanation:

The volume of a paraboloid is given by:
`V = (1/2)pi xx h xx r^2`

The volume of a cylinder is `V = pi xx h xx r^2`
THUS, for any given (h,r) the volume of the paraboloid will be `1/2` the volume of the cylinder:
`V_c = pi xx h xx r^2`
`V_p = (1/2)pi xx h xx r^2` ; `V_p = (½) V_c`