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

`V_(cylinder)=360\ cm^3`

`V_(cone)=(1)/(3)\cdot360\ cm^3=120\ cm^3`

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