I'm a student in Calculus class, and my teacher assigned us the following problem:
A cylinder is inscribed in a right circular cone of height $4$ and radius (at the base) equal to $6$. What are the dimensions of such a cylinder which has maximum volume?
The problem is I'm currently out of town, and the teacher is out of office. I've scoured my calculus book trying to find a similar problem to try and find a place to begin on this one, but I can't seem to find ANYTHING like it (a recurring issue in this class). I have a feeling it is an optimization problem but I honestly don't understand the question (how do you make a cylinder from a cone?).
Where do I even start with this problem? I feel that once I get a clearer understanding of what the question is asking, I'll be able to answer it on my own.