How do you find the radius of a cone knowing only the height and volume?

The volume v = (1/3) pi r2 h

You just need to rearrange this to get r on its own.

Multiply both sides by 3:

3v = pi r2 h

Divide both sides by pi:

3v / pi = r2 h

Divide both sides by h:

3v / (pi h) = r2

We get an answer for the radius which is the square root of 3v / (pi h)