Largest possible volume of a cylinder inscribed in a cone

[Calculus!]

Homework Statement

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.

 

[HallsofIvy]

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?

 

[Calculus!]

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

 

[Mark44]

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

From your first post:

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.

r and h are the dimensions of the cone. Follow Halls's suggestion to draw a picture and label the important points.