Kirara's Question from Yahoo Answers.

MHB
Thread starter Sudharaka
Start date Jun 7, 2012

In summary, to solve the given problem of creating a box with a square base and no top from a square piece of cardboard and holding 1000 inches cubed, the side length of the cardboard needs to be 24.91 inches by 24.91 inches. This can be determined by setting up an equation using the dimensions of the box and solving for the side length.

Jun 7, 2012

Sudharaka

Gold Member

MHB

Title: How do you solve this math problem?

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!

Hi Kirara, :)

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.

Last edited: Apr 26, 2013

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