Question

Please show work!!! 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?

A- 14
B-18
C- 26
D- 22

Answer 1

i would say A or d because when you divide 784/4=196/49/12 so the closes one would be a 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=4L2 ⇒196=L2 ⇒L=14. Now, what we want is the length of the original paper.

Answer 2

The original square of piece of paper,
with the cutting and folding lines would look like this:
You see 4 congruent squares cut out of the corners.
If the length of the sides of those squares is 4 inches,
then the height of the box will be 4 inches.
Let x be the length (in inches) of the side of the square (the bottom of the box).
The surface area of the bottom (in square inches) is x^2,
and the volume of the box, calculated as area of the bottom times height,
(in cubic inches) is 4x^2
So 4x^2 = 784---> x^2 = 784/4 ---> x = sqrt 196 = 14.
Answer:
14 inches
Hope this helps :)