# Kirara's Question from Yahoo Answers.

#### Sudharaka

##### Well-known member
MHB Math Helper
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.

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.

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