You have to make a square-bottomed, unlidded box with a height of three inches and a volume of approximately 42 cubic inches. You will be taking a piece of cardboard, cutting three-inch squares from each corner, scoring between the corners, and folding up the edges. What should be the dimensions of the cardboard to the smartest quarter inch?
since the bottom is square, you will be using a square piece of cardboard.
So, if the uncut piece is of side x. after the cut, you will have volume
v = (x-6)^2 * 3
Now, you want v=42, so solve
3(x-6)^2 = 42
(x-6)^2 = 14
x = 6+√14
so, after cutting and folding, the volume will be √14*√14*3 = 42posted by Steve