Question 775455: A box with a square base and no top is to be made from a square piece of cardboard by cutting 4 inch squares from each corner and folding up the sides. The box is to hold 100 inches cubed. How big a piece of cardboard is needed?
Answer by ankor@dixie-net.com(22740)   (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 cardboard by cutting 4 inch squares from each corner and folding up the sides.
The box is to hold 100 inches cubed. How big a piece of cardboard is needed?
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The card board will square, let s = the side of the cardboard
:
Cutting 4" squares will subtract 8" from the sides of the cardboard
The height of the box will = 4"
:
A volume equation (area of the base times the height)
(s-8)^2 * 4 = 100
4(s^2 - 16s + 64) = 100
divide both sides by 4
s^2 - 16s + 64 = 25
s^2 - 16s + 64 - 25 = 0
s^2 - 16s + 39 = 0
Factors to
(s-13)(s-3) = 0
s = 13 inches, the only solution that makes sense, the side of the square cardboard
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Check, subtract 8 from 13, 5 * 5 * 4 = 100
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