Question

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.

Answer 1

Disagree

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.