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

Answer:

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

Step-by-step explanation:

The formula of a volume of a cylinder:

$V=\pi r^2h$

The formula of a volume of a cone:

$V=\dfrac{1}{3}\pi R^2h$

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

Therefore we have the equation:

$\dfrac{1}{3}\pi R^2h=\pi r^2h$     divide both sides by πh

$\dfrac{1}{3}R^2=r^2$           multiply both sides by 3

$R^2=3r^2\to R=\sqrt{3r^2}\\\\R=r\sqrt3$