Problem 67 (difficulty: 4/10)

Which rectangular box has the greatest volume among the ones with given surface area?

Solution:

\(\displaystyle A=2(ab+ac+bc)=6\frac{ab+ac+bc}3{\geq}6\sqrt[3]{a^2b^2c^2}=6V^{2/3}. \)

Equality can occur only for \(\displaystyle ab=ac=bc\), i.e. for the case of the cube.

Give me another random problem!