SOLUTION: A box with a square base and no top is to be made from a square piece of carboard by cutting 8 in. squares from each corner and folding up the sides. The box is to hold 20000 in cu

Algebra ->  Rectangles -> SOLUTION: A box with a square base and no top is to be made from a square piece of carboard by cutting 8 in. squares from each corner and folding up the sides. The box is to hold 20000 in cu      Log On


   

Question 1093890: A box with a square base and no top is to be made from a square piece of carboard by cutting 8 in. squares from each corner and folding up the sides. The box is to hold 20000 in cubed. How big a piece of cardboard is needed?
Please try to make things as clear as possible. Thank you for any help!!! I really appreciate it!!
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
A box with a square base and no top is to be made from a square piece of carboard by cutting 8 in. squares from each corner and folding up the sides. The box is to hold 20000 in cubed. How big a piece of cardboard is needed?
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Let the cardboard piece have length and width of x
Draw that square so you can see what is happening.
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You cut 8" by 8" squares from each corner and fold up
the remaining side pieces to form a box with no top.
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The base of that box is x-2*8 = x-16 inches by x-16 inches
The height of that box is 8.
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So the volume of that box is 8*(x-16)^2 = 20000 sq in
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Solve for x::
(x-16)^2 = 20000/8 = 2500
x-16 = 50
x = 66 inches
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The dimensions of the square are 66" by 66"
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Cheers,
Stan H.
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