Question

The sphere that can be placed in a right cylinder whose height equals to its diameter has a maximum volume of 972pi cm^3. Find the volume of the cylinder.

Answer 1

It is clear that the height of the cylinder is equal to its diameter. We need to find this value to get the volume of the cylinder.

What we have here is the volume of the sphere which depends only on the diameter of the sphere. So we can get the diameter of the sphere from its volume. Find it.

Then, the sphere is placed in the cylinder. This means that the diameter of the cylinder must be equal (at least) to the diameter of the cylinder. Since we have the diameter of the sphere calculated, we can now calculate the volume of the cylinder.