Find the dimensions of a square piece of cardboard given data of it folded into a square (cubic inches, etc.)

Question

A box with a square base and no top is to be made from a square piece of cardboard by cutting 6 in. squares out of each corner and folding up the sides. The box needs to hold 1000 in3 . How big a piece of cardboard is needed?

Answer 1

1. Let $x$ be the side length of the cardboard before cutting.
2. Determine the dimensions of the box in terms of $x$.
3. Use the results of step 2 to write the volume of the box in terms of $x$.
4. Set the expression from step 3 equal to 1000 and solve for $x$.