Question

a cylinder has a volume of 72 inches. what is the volume of a cone with the same height and radius as the cylinder? Explain

Answer 1

The formula of a volume os a cylinder:

`V=\pi r^2H`

r - radius

H - heihgt

The formula of a volume of a cone:

`V=(1)/(3)\pi r^2H`

r - radius

H - height

If a cylinder and a cone have the same radius and height then the volume of a cone is three times smaller than a volume of a cylinder.

Therefore

`V_(cone)=(1)/(3)V_(cylinder)`

We have

`V_(cylinder)=72\ in^3`

Substitute:

`V_(cone)=(1)/(3)\cdot72=24\ in^3`

Answer: The volume of a cone is 24 in³.