A cylinder is inscribed in a right circular cone of height 4.5 and radius (at the base) equal to 5.5. What are the dimensions of such a cylinder which has maximum volume?

Question

I am looking for the radius and height.

Answer 1

Note that the volume of a cylinder =πr²h where r=radius and h= height. Note further that the surface of the cone can be described as y=4.5-4.5x/5.5. If we substitute y for h and x for r in the formula for the volume of the cylinder we get Volume = πx²(4.5-4.5x/5.5). Find dV/dx and set =0 to find x=11/3 and y=1.5 thus the Volume = 63.4