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 to hold 16128 in3. How big a piece of cardboard is needed?

Your answer is ?in by ?in

Ooops, I think I put this up in the wrong category. If anyone could help me asnwer this, that would be great! :)

math help needed

I tried math help, but no one has responded :(

To solve this problem, we need to find the dimensions of the square piece of cardboard needed to make the box.

Let's call the side length of the square cardboard x inches.
When we cut 7-inch squares from each corner, the side length of the base of the box will be reduced by 14 inches (7 inches from each corner).
So, the side length of the base of the box will be (x - 14) inches.

When we fold up the sides, the height of the box will be 7 inches.

The volume of a rectangular prism (which in this case is the box) is given by the formula:

Volume = Length * Width * Height

In this case, Length and Width are equal to the side length of the base of the box, which is (x - 14) inches. And the Height is 7 inches.

So, the equation to find the volume of the box is:

16128 = (x - 14) * (x - 14) * 7

To solve this equation, we can divide both sides by 7 to simplify it:

2304 = (x - 14) * (x - 14)

Now we can take the square root of both sides to solve for x:

48 = x - 14

Adding 14 to both sides:

x = 62

Therefore, the side length of the square cardboard needed to make the box is 62 inches.

So, the size of the cardboard needed is 62 inches by 62 inches.