Question

Item 17 A sphere and a right cylinder have the same radius and volume. Find the radius rr in terms of the height hh of the cylinder.

Answer 1

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.