Open the Box

Weekly Problem 37 - 2015
A piece of card is folded to make an open box. Given its surface area, can you work out its volume?
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Problem

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Open the Box


A square piece of card has a square of side $2$ cm cut out from each of its corners. The remaining card is then folded along the dotted lines shown to form an open box whose total internal surface area is $180$ cm$^2$.

What is the volume of the open box in cm$^3$?

If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.