SOLUTION: A rectangular sheet of cardboard was used to make a pencil box. Four (4) small squares were removed, one from each corner of the cardboard, to create the base of the box with dimen

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Question 1078700: A rectangular sheet of cardboard was used to make a pencil box. Four (4) small squares were removed, one from each corner of the cardboard, to create the base of the box with dimensions 55 cm by 30 cm. When the cardboard is folded to make the pencil box, it is found that it has a capacity of 3,150 cm3. What are the dimensions of the original sheet of cardboard that was used to make the pencil box?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Original dimensions of cardboard before corners cut, x and y.
u, the edge length of square to cut from each corner; also u becomes the height of the box.

Base dimensions already give, 55 and 30.

55%2A30%2Au=3150, using given volume.
u=21%2F11=1%2610%2F11


Two of u is cut on each cardboard dimension.
x-2u=55
x=55%2B2u
x=55%2B2%2821%2F11%29
x=58%269%2F11
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y=2%2821%2F11%29%2B30
y=33%269%2F11
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highlight%28system%28x=58.82%2Acm%2Cy=33.82%2Acm%29%29