Example 1As you can see, this question is hard enough even with the formulas provided. This is no mere
matter of plugging values into a formula and cranking out the answer. This question is more
algebraic than that and takes a little thought. It’s really a word problem. It describes in words a
mathematical (in this case, geometric) situation that can be translated into algebra.
The pivot in this situation is that the cone and sphere have equal volumes. You’re looking for the
radius of the sphere in terms of x, the radius of the cone, and fortunately you can express both
volumes in terms of those two variables. Be careful. Both formulas include an r, but they’re not the
same r’s—the cone and the sphere have different radii.
A right circular cone and a sphere have equal volumes. If the cone has radius x and height 2x,
what is the radius of the sphere?1.
(A) x(B)