# Largest possible volume of a cylinder inscribed in a cone

1. Dec 4, 2008

### Calculus!

1. The problem statement, all variables and given/known data

A right circular cylinder is inscribed in a cone with height h and base radius r. Find the largest possible volume of such a cylinder.

I'm just really confused on how to figure this one out. The equation for the volume of a cone is v = 1/3pi r^2h and the volume of a cylinder is v = pi r^2h. I just don't know how to use these two formuals in order to find a solution. Please help me. Thanks.

2. Dec 4, 2008

### HallsofIvy

Staff Emeritus
Re: Optimization

Draw a picture. Draw a coordinate system so and two lines, one through (r, 0) and (0, h) and the other through (-r, 0) and (0, h). That represents your cone. What are the equations of the lines? A cylinder inside the cone is represented by a rectangle in your picture. What are the dimensions of that cylinder?

3. Dec 4, 2008

### Calculus!

Re: Optimization

The problem didn't state any dimesions or equations for the cylinder or cone.

4. Dec 5, 2008

### Staff: Mentor

Re: Optimization