Pharaoh has decided he doesn't like his pyramid and wants a new one, following the conventional square-based design, but faced with with brilliant white marble that will sparkle in the sunlight. Trouble is, brilliant white marble comes at a hefty prices, and just at the moment the palace coffers are running a bit low.
So he calls in the palace mathematicians and asks them how to make the volume of his new pyramid as large possible for a given amount of marble. What is the optimal ration between the pyramids height H and the base length L of its sides?
Solution at the end of the week.