Question

The volume of a cylinder is 32.25 cubic inches. If a cone has the same height and radius as the cylinder, what is its volume?

Answer 1

The volume of a cylinder with a radius r and a height h:

`V_1=\pi r^2h`

The volume of a cone with a radius r and a height h:

`V_2=(1)/(3)\pi r^2h`

Therefore

`V_2=(1)/(3)V_1`

We have
`V_1=32.25\ in^3`

Substitute:

`V_2=(1)/(3)\cdot32.25=10.75\ in^3`

Answer: The volume of a cone is equal 10.75 in³