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:

$V=\dfrac{1}{3}\pi r^2H$

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

$V_{cone}=\dfrac{1}{3}V_{cylinder}$

We have

$V_{cylinder}=72\ in^3$

Substitute:

$V_{cone}=\dfrac{1}{3}\cdot72=24\ in^3$

Answer: The volume of a cone is 24 in³.