A box with a square base and no top is to be made from a square piece of carboard by cutting 2 in. squares from each corner and folding up the sides.

Question

A box with a square base and no top is to be made from a square piece of carboard by cutting 2 in. squares from each corner and folding up the sides. The box is to hold 648 in³. 

How big a piece of cardboard is needed?

Your answer is: ______ in. by ______ in.

THANK YOU!

Answer 1

The height of the box will be 2 in., so the area of the square base is 648/2 = 324, so each side is sqrt(324) = 18. Note, though, that 2 in. more on each side, so the cardboard is 18+2*2 = 22 in on each side;

22 in. by 22 in.

(By the way, 22^2 - 4 * 2^2 (the corners) - 18^2 = 144; this equals 18* 2 * 4, the 4 sides)