SOLUTION: A square piece of cardboard is to be formed into a pizza box. The box is formed by cutting 2-inch square corners from the cardboard and folding them up. If the volume of the box is
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Question 144121: A square piece of cardboard is to be formed into a pizza box. The box is formed by cutting 2-inch square corners from the cardboard and folding them up. If the volume of the box is 512 in^3, what are the dimensions of the cardboard?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
The side of the cardboard square: x
The length and width of the box: x - 4 (because you need to subtract 2 inches from each side)
The height of the box: 2
Volume of the box
Multiply the binomial and divide both sides by 2:
or . Exclude the negative root as extraneous and not meaningful since we are looking for a positive measure of length. The original cardboard was then 20 inches by 20 inches.
Check:
Cut out 2 inch squares from the corners of a 20 X 20 piece of cardboard and then fold up the sides, making a 16 by 16 by 2 box. Checks.
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