Question

In order to make a box, James cut out four small 2 by 2 squares from each corner of a square piece of cardboard. If the volume of the box he made is 50 inches cubed, what is the length of a side of the original square?

Please help, thanks.

Answer 1

9 inches.

Explanation:

Let the length of the square cardboard =x inches

If James cut out four small 2 by 2 squares from each corner of a square piece of cardboard.

In the attached diagram, the box is folded along the green dotted line.

Therefore:

• Length of the box =(x-4) inches
• Width of the box =(x-4) inches
• Height of the box =2 inches

Volume of a rectangular prism=LWH

Volume =50 inches cubed

Therefore:

2(x-4)(x-4)=50

Divide both sides by 2

`(x-4)^2=25\\(x-4)^2=5^2\\x-4=5\\x=5+4\\x=9$ inches`

Therefore, the length of the original square is 9 inches.