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?

1 Answer
Nov 7, 2015

Answer:

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#