Math CentralQuandaries & Queries


Question from tina, a student:

I need help solving the following:

An open box is to be made from a rectangular piece of tin by cutting two inches squares out of the corners and folding up the sides. The volume of the box will be 100 cubic inches. Find the dimensions of the rectangular piece of tin.

Hi Tina. There is a problem with the question you wrote. I'll show you why.

If I cut two inch squares from the corners and fold up the sides, I have a height of 2 inches, right?

Now I am told that the volume will be 100 cubic inches. So if I multiply width x length x height I will get the volume. That means that if I divide the volume by the height, I get width x length. In this case, volume divided by height is 100 / 2 = 50.

So I know that the width times the length of the bottom of the box is 50. But there are many possible ways to multiply two numbers to get 50!

It could be 5 x 10 on the bottom, 2 x 25, or even 4 x 12.5. Of course the original piece of time would be 4 inches wider and 4 inches longer because of the sides you fold up.

But there's no one answer to the question as you've written in.

Stephen La Rocque


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