Posted by Amy on .
Show that a rightcircular cylinder of greatest volume that can be inscribed in a rightcircular cone that has a volume that is 4/9 the volume of the cone.
Please, help out, this is for a study guide for a quiz. :) Thank you.

Calculus 
Reiny,
Amy, take a look at the solution I gave to the first of the "Related Questions" below.
It is the same kind of question except it has specific values.
Instead of a height of 12 and a radius of 4 for the cone, in your question you would have a height of H and a radius of R, where H and R are constants, that is, they are fixed values.
See if you can follow the same steps, then take the volume of the cone and the volume of the cylinder.
They should be in the ratio of 4:9
Get back to me if you run into problems, but give it a try.