It might be easier for you to visualize a cross-section of the cone, which looks like an isosceles triangle. Now, you want to find an equation for the volume of the cylinder that uses just one variable, and the easiest choice for this variable is the radius of the cylinder. The cross-section of the cylinder will look like a rectangle. Now, as the cylinder gets wider (via an increasing radius), it also gets shorter. The height of the cylinder is dependent on the radius, as you have noted. The exact relationship is linear: . Once you see that it is a linear relationship, that equation is fairly easy to derive. So the volume of the cylinder will be . Can you take it from there?