SOLUTION: A box is formed by cutting squares from the four corners of a sheet of paper and folding up the sides.
a. Suppose the paper is 5"-wide by 7"-long
What is the maximum volume f
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Question 1122304: A box is formed by cutting squares from the four corners of a sheet of paper and folding up the sides.
a. Suppose the paper is 5"-wide by 7"-long
What is the maximum volume for the box?
What cutout length produces the maximum volume?
b. Suppose we instead create the box from a 7"-wide by 9"-long sheet of paper.
-What is the maximum volume for this box?
-What cutout length produces the maximum volume?
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!
Let x be the length of the side of the square that is cut out of each corner; then the depth of the box will be x.
a. If the original sheet of paper is 5x7 inches, then the length and width of the box will be (5-2x) and (7-2x). The volume of the box will then be
The maximum volume, and the length of the edges of the cutout corner squares will not be "nice" numbers.
You can use a graphing calculator to find a decimal approximation to the answer.
If you need an exact answer, you can find the derivative of the volume function (which will be a quadratic function) and use the quadratic formula to find the exact irrational answer.
b. For different dimensions of the original piece of paper, perform the same steps with the new volume function. Again the answers will not be "nice" numbers....
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