Question

A cylinder has a volume of 360 cubic centimeters. Find the volume of a cone with the same height and diameter as the cylinder.

Answer 1

The formula of a volume of a cylinder:

$V_{cylinder}=\pi r^2H$

The formula of a volume of a cone:

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

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

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

$V_{cylinder}=360\ cm^3$

$V_{cone}=\dfrac{1}{3}\cdot360\ cm^3=120\ cm^3$

Answer: The volume of a cone is equal 120 cm³.