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  1. You need to ship USB cables in a small cardboard square-based prism box. The box must have a capacity of 750 cm3 but use the smallest amount of cardboard.

a) What are the dimensions of the box? (2 decimal places) b) How much cardboard will you be using? (1 decimal place)

So I basically need help on how I start to answer this question, step by step. I am confused on how to get these answers with only the information provided.

Chelsea
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    In general, if you're not sure where to begin, write down the relevant equations and fiddle with them until you have a better understanding of the problem. In this case, the formulas for the surface area and the volume of a square-based prism with edge $x$ and height $y$ will be helpful: $A=2x^2+4xy$ and $V=x^2y$. – Ant Jan 08 '18 at 02:19

1 Answers1

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If you wanted to fence off a quadrilateral area with a limited amount of fence, but want to maximize your area fence off, what is the best shape to make the fence?

Square

Extending this to the third dimension, the most efficient way to get 750cm3 in a box with the least amount of cardboard would be to make a

Cube

So, the dimensions would be cube root 750, or

9.09 cm by 9.09 cm by 9.09 cm

and the surface area would be

54.5 cm

T. Rowaway
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