“An equilateral triangle and a square are inscribed in a circle, with a side of the triangle being parallel to a side of the square. The entire figure is revolved about that altitude of the triangle which is perpendicular to a side of the square. Find the ratio of the area of the sphere to the total area of the cylinder, and the ratio of the total are of the cylinder to the total are of the cone”.

I seem to get the right result for the ratio sphere / cylinder, but not the second one. In this problem the cylinder has height = diameter, therefore we can get the sphere’s diameter (cylinder’s diagonal) using the Pythagorean theorem and then working through the rest.

When I deal with the cone, I would be tempted to use the same logic, as the diameter of the cone should be the same as the cylynder’s.

Any hints?