# Math Help - Find Ratios Between Volumes + Extra

1. ## Find Ratios Between Volumes + Extra

I got this question for homework and I'm not sure how to do it:

a) Find the ratio between the volume of a cone and the volume of a sphere.

b) Find the values of r and h if the ratio in a) = 1/3.

Thanks a lot.

2. Volume of a cone is $\frac {1}{3}\pi r^2h$, Where r is the radius of the base and h is the height of the cone.

Volume of a sphere is $\frac {4}{3}\pi r^3$.

To find the ratio, divide the cone formula by the sphere formula:

$\frac {\frac {1}{3}\pi r^2h}{\frac {4}{3}\pi r^3}$

Factor out $\frac {1}{3}\pi r^2$ from the top and bottom:

$\frac {(\frac {1}{3}\pi r^2)(h)}{(\frac {1}{3}\pi r^2)(4r)}$

$\frac {h}{4r}$