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23 February, 14:14

Brad wants to package his baseballs in sets of 100. Bethany says the box that will take least amount of cardboard for 100 baseballs is one with a base of 2*5 and a height of 10. Do you agree or disagree? Explain your thinking.

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  1. 23 February, 15:18
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    Disagree

    Step-by-step explanation:

    A box with minimum area for a given volume will have the shape of a cube. The cube root of 100 is about 4.64, so a box that is about 4*5*5 will probably have a smaller area.

    I gross terms, the 2*5*10 box will have area

    ... 2 (2*5 + 10 * (2+5)) = 160 square units

    where a unit may be a baseball diameter.

    On the other hand the 4*5*5 box will have an area of ...

    ... 2 (4*5 + 5 * (4+5)) = 130 square units

    Since baseballs can be close-packed, the box may be able to be made smaller than the above suggested dimensions might indicate.
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