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- Feb 5, 2012

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**Title: How do you solve this math problem?**

Hi Kirara,A box with a square base and no top is to be made from a square piece of cardboard by cutting 6 in squares from each corner and folding up the sides. The box is to hold 1000 in^3(inches cubed). how big a piece of cardboard is needed?

I know that the answer is 24.91 in by 24.91 in but i can't figure out how to get this answer.

Please help!

Let \(x\) be the side length of the cardboard. We cut \(6\mbox{ inch}\) squares from each corner. Therefore the side length of the base becomes \(x-12\). The height of the box is \(6\mbox{ inches}\). Therefore it's volume will be, \(6(x-12)^2\). Since it is given that the box should hold \(1000 \mbox{ inch}^3\),

\[6(x-12)^2=1000\]

\[x=12+\sqrt{\frac{1000}{6}}\approx 24.91\mbox{ inches}\]

Best Regards,

Sudharaka.

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