1. What are the dimensions of the right hexagonal prism of minimum surface whose volume is 36 cubic feet?
2. Find the dimension of the rectangle of maximum area that can be inscribed in the ellipse (b^2)(x^2)+(a^2)(y^2)=(a^2)(b^2)
3. A right cone of maximum volume is inscribed in a given right cone, the vertex of the inside cone being at the center of the base of the given cone. show that the altitude of the inside cone is one third the altitude of the given cone.