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?

Question

asked Mar 2, 2021 115k views

1 Answer

Kuza · Answer 1 · 2021-03-07T07:39:45+0000

Answer:

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.

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

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.