Sphere and right cyl. have the same radius and volume. Thus, find the equations for the volumes of a sphere and a right cylinder and set them equal to one another:
Vol. of sphere = Vol. of right cyl.
(4/3) pi r^3 = pi r^2 * h
"pi" appears on both sides of this equation as "pi." So we can cancel "pi" from both sides. We then have:
(4/3) r^3 = r^2 h
Let's now divide both sides of this new equation by r^2. We then have:
(4/3) r = h
We must solve this for r in terms of h. To do this, multiply both sides of this equation by (3/4). This results in:
r = (3/4) h This is the final answer: the radius, r, in terms of the height, h.