Please help! Need to show work. So lost. Don't even know where to begin!!

Question

A box with a square base and no top is to be made from a square piece of cardboard by cutting 4 in. Squares from each corner and folding up the sides. The box is to hold 100 in "cubed". How big a piece of cardboard needed?

Answer 1

The box is a rectangular prism with a square base. Draw a picture to help yourself, Once of the box and one of the cardboard square.

Since you cut four inches on both sides of the cardboard on all sides. Each side of the cardboard will be s + 8,
with s = one side of the square base of the box.

If you imagine the cardboard with cuts correctly, you will find that the remaining length of each side of the cardboard square after cutting 4 inches off on both ends will be one side of the square base of the box.

You will find that the box with a height of 4 in.

Therefore the volume of the box must be:

V = lwh = l * w * 4 = 100
so l * w = 25.

REMEMBER THE BOX HAS A SQUARE BASE.

l * w = s² = 25
so s = 5

Therefore s + 8 = 13.

Area of cardboard square =  13 * 13 = 169 in²