# 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?

Nov 7, 2015

22 inches

#### Explanation:

$V = L \cdot W \cdot H$

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.

$L = W$

$\implies 784 = 4 \cdot L \cdot W$
$\implies 784 = 4 {L}^{2}$
$\implies 196 = {L}^{2}$
$\implies L = 14$

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

$\implies L ' = 14 + 4 + 4$
$\implies L ' = 22$