How to find the following answers?

Question

Determine the dimensions of the right circular cylinder, with the greatest volume, that can be

inscribed in a right circular cone with base radius R and altitude H.

Answer 1

The steps involved in this optimization problem are explained in the video, The radius of the cylinder with maximum volume would have to b e 2/3 the radius of the cone and the height of the cylinder would then be 1/3 the height of the cone.