I have enough pure silver to coat 2 square meters of surface area.
I plan to coat a sphere and a cube, and to use all of the silver in doing so.
Allowing for the possibility of all of the
silver going onto one of the solids, what dimensions should they be if the
total volume of the silvered solids is to be a maximum?

The radius of the sphere is

and the length of the sides of the cube is

Again, allowing for the possibility of all of the silver going onto one of the
solids, what dimensions should they be if the total volume of the silvered
solids is to be a minimum?

The radius of the sphere is

and the length of the sides of the cube is

You can earn partial credit on this problem.