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

To solve this problem, we start with a square piece of cardboard with side length inches. After cutting out 6-inch squares from each corner, the dimensions of the base of the box become inches for each side (since we cut 6 inches from both ends of the square).

When we fold up the sides, the height of the box is 6 inches. The volume of the box can be expressed as:

This can be simplified to:

We know that the volume of the box is 5046 cubic inches, so we set the equation to:

Dividing both sides by 6 gives:

Taking the square root of both sides results in:

So, we find:

The original piece of cardboard should be 41 inches by 41 inches.

So, the final answer is:

in. by .