A box with a square base and no top is to be made from a square piece of carboard by cutting 7 in. squares from each corner and folding up the sides. The box is

Question

(question continued)to hold 847 in^3. How big a piece of cardboard is needed?

Answer 1

The box need not be a cube. It must have a square base, and 7 inch squares are to be cut from each corner of a square piece. Thus, each side of the original square must be 7+x+7 inches long. "X" will turn out to be the height of the rectangular prism to be created which has 2 parallel square bases.

 

So, calculating the volume, we have x * x * 7 = 847 cubic inches, or x^2 = 121 square inches. Thus x = 11 inches. So the original square must be 25 inches on each side. After the 7 inch squares are cut from each corner, it leaves 4 11-inch long flaps sticking out to be folded upwards.

 

The final box has a square base with 11 inches on each side, it is 7 inches in height, and the final volume is 847 cubic inches.

Answer 2

Lets say each side of the base is "a" so 7 x a^2 = 847, then a =11, if you draw it, you will find the answer. HInt: 7+11+7=