Question

A cone and cylinder have the same height and their bases are congruent circles. If the

volume of the cylinder is 120 in3, what is the volume of the cone?

Answer 1

40 in³

Explanation:

You want the volume of a cone if the volume of a cylinder with the same radius and height is 120 in³.

Formulas

The formulas for the volume of a cylinder and cone are ...

V = πr²h . . . . . volume of a cylinder with radius r and height h

V = 1/3πr²h . . . . . volume of a cone with radius r and height h

Cone volume

If the volume of the cylinder is such that ...

πr²h = 120 in³,

we can substitute for πr²h in the formula for the volume of the cone:

V = 1/3πr²h = 1/3(120 in³) = 40 in³

The volume of the cone is 40 in³.