Question 57499: A rectangular sheet of cardboard has a square of the same size cut from each of its corners. Then the sides are folded upward to make a topless box. The width of the uncut cardboard sheet is 3/4s of its length, and a total of 64 square inches of cardboard is cut from the four corners. What is the volume of the box if the area of its base is 1,120 square inches? What are the demensions of the uncut cardboard sheet?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A rectangular sheet of cardboard has a square of the same size cut from each of its corners. Then the sides are folded upward to make a topless box. The width of the uncut cardboard sheet is 3/4s of its length, and a total of 64 square inches of cardboard is cut from the four corners. What is the volume of the box if the area of its base is 1,120 square inches? What are the demensions of the uncut cardboard sheet?
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Find out the value of the cardboard squares that are cut out of the corners:
"total of 64 square inches of cardboard is cut from the four corners."
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Each corner uses 64/4 = 16 sq inches. The dimensions of the those squares:
SqRt(16) = 4 inches
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Let the length of the cardboard square = x
It says the width is 3/4 of the length: width = .75x
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The dimensions of the bottom of the box: (x-8) by (.75x-8). Find it's area:
:
(x-8)*(.75x-8) = 1120
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Foil: .75x^2 - 8x - 6x + 64 = 1120
.75x^2 - 14x + 64 - 1120 = 0
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A quadratic equation:
.75x^2 - 14x - 1056 = 0
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Solve this using you favorite method, I used a basic program that I wrote for this purpose. The positive solution: x = 48"
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Box length = 48 - 8 = 40"
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Box width is .75(48)- 8 = 28:
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The height wouLd be 4"
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Find the box vol = 4 * 40 * 28 = 4480 cu in
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The diminsions of the original piece of cardboard: 48" by 36"
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Check using the given area of the bottom square of the box:
(48-8)(36-8)
40 * 28 = 1120:
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Hope this made some sense to you.
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