. Find the ratio of: The volume of the smaller cone to the volume of the frustum

Question

A cone is cut by a plane parallel to the base, 1/ 5 of the way up the height of the cone (from the base), resulting in a smaller cone and a frustum. Find the ratio of: The volume of the smaller cone to the volume of the frustum

Answer 1

Hi Ben C.,

What I suspect you need, are the tools to solve this problem, rather than the solution itself?

You need to know that the volume of a cube is (1/3)*b*h

so for similar-central-angle cones, such as the nested pair here, this translates into : V = ar^3 where a is a constant.

So the smaller cone has (4/5)^3 the volume of the larger cone, since it has a (4/5) scale factor for r. All the rest is just bookkeeping.

-- CHeers, --Mr. d.

Answer 2

The volume of the cut off cone is 64 / 125 of the whole cone.

That leaves 61 / 125 for the frustum.

What is the ratio of the volume of the cone to that of the frustum?