SOLUTION: A box without a top is to be made by cutting squares measuring 8 cm on a side from each corner of a square piece of tin and folding up the sides. Find the dimensions of the box, i

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Question 181942: A box without a top is to be made by cutting squares measuring 8 cm on a side from each corner of a square piece of tin and folding up the sides. Find the dimensions of the box, if it is to have a volume of 9248cm cubed.

Answer by nerdybill(7384) About Me  (Show Source):
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A box without a top is to be made by cutting squares measuring 8 cm on a side from each corner of a square piece of tin and folding up the sides. Find the dimensions of the box, if it is to have a volume of 9248cm cubed.
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Your best bet is to draw a diagram of the problem and jot down all the information provided. It'll help you "see" the problem better.
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Let x = length of one side of square piece of tin
then
length = width = x-2(8) = x-16
height = 8
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(x-16)(x-16)8 = 9248
(x-16)(x-16) = 1156
x^2 - 32x + 256 = 1156
x^2 - 32x - 900 = 0
(x+18)(x-50) = 0
x = {-18, 50}
Tossing out the negative value we have:
x = 50 cm
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width = x-16 = 50-16 = 34 cm
length = x-16 = 50-16 = 34 cm
height = 8 cm
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Dimensions of box:
34 cm X 34 cm X 8 cm