Question

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A flat, square piece of cardboard is used to construct an open box by cutting out squares (measuring 1 foot by 1 foot) from the corners and folding up the resulting edges. If a particular box has a volume of 64 cubic feet, what are the dimensions of the original piece of cardboard?

The dimensions of the original piece of cardboard are feet ____by ___________ feet.

Answer 1

Ok, we can use the volume of the box to get the length of the box. Simply find the cubic root of 64.

Then since we know that the box is folded, and the folded sections are 1 foot long on each side, if we unfold the box we will add 2 to the length of the box. This is the length of the original cardboard square.

Answer 2

Cubic root of 64 will not give correct answer, here's why:-
Since 1x1 squares were cut from corners & sides folded the height of open box is 1 foot. But originally it was a square sheet, therefore the length & width of the open box are same.
So if the length (or width) of box is L, the volume is,
L* L* 1 = 64
therefore , L = 8 feet
finally, the original sheet was longer by 2 feet, since 1 foot each was shortened from each side.
therefore original sheet size was 10 feet x 10 feet.