SOLUTION: If a total of 1700 square centimeters of material is to be used to make a box with a square base and an open top, find the largest possible volume of such a box. The box is draw

Algebra ->  Rectangles -> SOLUTION: If a total of 1700 square centimeters of material is to be used to make a box with a square base and an open top, find the largest possible volume of such a box. The box is draw      Log On


   

Question 856837: If a total of 1700 square centimeters of material is to be used to make a box with a square base and an open top, find the largest possible volume of such a box.
The box is drawn 3-D with no top, the right face and front face of the box has an x and along the left corner is the h.
Could you help me?
Thank you,
Ashley Dodson
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
The square base makes this a simpler problem than if no side were square.

x = side of base edge
y = height

AREA ACCOUNTING FOR 1700 SQUARE CM
The base area is x%5E2; and there are FOUR surfaces of xy cm%5E2, so 4xy cm%5E2.
Altogether, the area equation is highlight_green%284xy%2Bx%5E2=1700%29.

VOLUME FORMULA
v for volume, highlight_green%28v=%28x%5E2%29y%29.

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Can you understand that analysis?
Can you continue from there yourself?
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After almost completing the solution myself, the problem question is either for College Algebra or for first semester of Calculus. If for College Algebra, you might use a graphing calculator to find the maximum point. If Calculus, then you would differentiate v against x, solve for x if the derivative is zero, and that will be the x value for maximum volume, v. The process should bring you to %28d%2F%28dx%29%29v=425-%283%2F4%29x%5E2=0.