Question

A solid consists of a cone on top of a cylinder with a radius equal to that of the cone. The height of the cone is `36` and the height of the cylinder is `8`. If the volume of the solid is `64 pi`, what is the area of the base of the cylinder?

Answer 1

20.1

Explanation:

A Conical Volume is given by:
`V = 1/3 * pi * r^2 * h`
A Cylindrical Volume is given by:
`V = pi * r^2 * h`
Circular Area (base of cylinder)
`A = 2*pi * r^2`

Total solid volume =
`64pi = 1/3 * pi * r^2 * h_1 + pi * r^2 * h_2`

Solve for r.
`64 = 1/3 * r^2 * 36 + r^2 * 8` ; `64 = r^2 * 12 + r^2 * 8`
`64 = r^2 * 20` ; `64/20 = r^2` ;

`r^2` = 3.2 ; r = 1.79

`A = 2*pi * 3.2 = 20.1`