SOLUTION: Imagine a piece of square paper that measures 20 by 20 cm. You can make a box with no lid by cutting a square of the same size from each corner and folding up what's left. Keeping

Question 984998: Imagine a piece of square paper that measures 20 by 20 cm. You can make a box with no lid by cutting a square of the same size from each corner and folding up what's left. Keeping the length of each side integers, what is the maximum volume box that can be made?
I'm not sure where to begin, any help is greatly appreciated.
Found 2 solutions by Alan3354, solver91311:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Imagine a piece of square paper that measures 20 by 20 cm. You can make a box with no lid by cutting a square of the same size from each corner and folding up what's left. Keeping the length of each side integers, what is the maximum volume box that can be made?
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Begin here.
If you cut out squares of x by x and fold it up, what is the volume?

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

If you cut by out of each corner and fold up the sides, the measure of the sides of the square bottom of the box will be by and the measure of the depth of the box will simply be . So:

but this function has a restricted range because any value of smaller than zero or larger than 10 is absurd, while or results in a zero volume box. Given these restrictions, and the problem requirement of , the possible answers are one of the numbers 1 through 9 inclusive. You could try each of these nine possibilities in the volume function to see which one gives you the largest answer, or you could look at a graph of the function and perhaps narrow your search somewhat.

.

John

My calculator said it, I believe it, that settles it

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