Some airlines have restrictions on the size of items of luggage that passengers are allowed to take with them. Suppose that one has a rule that

Question

the sum of the length, width, and height of a y piece of luggage must be less than or equal to 210 cm. A passenger wants to take a box of the maximum allowable volume. If the length and width are equal, what should the dimensions be?

Answer 1

70 by 70 by 70 cm gives max volume = 343,000 cm^3

a cube has minimum surface area for a given volume with h=w=L

and max volume for given surface area

3 times 70 =210