Question

A cylinder is inscribed in a right circular cone of height 8 and radius (at the base) equal to 5. What are the radius and height of such a cylinder which has maximum volume?

Answer 1

Write an equation for the volume of the cylinder in tems of its radius, r. Let R be the constant radius of the base of the cone. You need to use some analytic geometry to get the height of the cylinder in terms of r. The relationship between r and h is
h = (8/5)(R-r)
Write V(r) for the cylinder and find the r and h(r) values where the derivative is 0.