Question

An open box is formed by cutting squares with side lengths of 4 inches from each corner of a square piece of paper. What is a side length of the original paper if the box has a volume of 784 cubic inches?

Answer 1

22 inches

Explanation:

`V = L * W * H`

Since 4 inches were cut from each corner of the square piece of paper, we have

`H = 4`

Since the original paper is square and the length cut from each side is the same, the resulting base is still square.

`L = W`

`=> 784 = 4 * L * W`
`=> 784 = 4L^2`
`=> 196 = L^2`
`=> L = 14`

Now, what we want is the length of the original paper.
Since we folded the paper from each side, we need to add the length of opposite sides (i.e. 2 instances) of the folded part to get
the original length

`=> L' = 14 + 4 + 4`
`=> L' = 22`