Question

The formula for the volume of a cylinder is V = πr2h. The volume of a cylinder is three times the volume of a cone with the same radius and height.

If the volume of a cone with the same height as a cylinder equals the volume of the cylinder, the equation for the radius of cone R in terms of the radius of cylinder r is
.

Answer 1

`\large\boxed{R=r\sqrt3}`

Explanation:

The formula of a volume of a cylinder:

`V=\pi r^2h`

The formula of a volume of a cone:

`V=(1)/(3)\pi R^2h`

The volume of a cone is equal the volume of a cylinder.

Therefore we have the equation:

`(1)/(3)\pi R^2h=\pi r^2h` divide both sides by πh

`(1)/(3)R^2=r^2` multiply both sides by 3

`R^2=3r^2\to R=√(3r^2)\\\\R=r\sqrt3`