Show that the maximum volume of a cylinder of radius r which can be cut centrally from a right solid cone of height h and semi-vertical angle alpha is givenby (4pi/27)h^3tan^2alpha

Question

Show that the maximum volume of a cylinder of radius r which can be cut centrally from a right solid cone of height h and semi-vertical angle alpha is givenby (4pi/27)h^3tan^2alpha

Answer 1

google cylinder inscribed in cone and you will find may expositions of a cylinder inscribed in a cone of base radius R and height h.

The only twist to your problem is that you have h and α instead of h and R.

If you draw a side view, it its clear that

R/h = tan α

Now work with that in the solved examples.