12 cans are pack in rectangle boxes in 3 by 4 or 3 by 2 by 2. Each has a diameter of 6.5 cm and a height of 12.5 cm. Which arrangement uses the least amount of packaging material.

Question

I'm not sure but I think they both use the same amount of material

and the 3 by 4 means 3  rows by 4 columns

and 3 by 2 by 2 means 3 rows by 2 columns by 2 layers.

plus they are rectangular boxes

Answer 1

We can consider the space taken up by each can is cuboid with dimensions 6.5*6.5*12.5.

If packed in a single layer, the box dimension would be 3*6.5 by 4*6.5 by 12.5. This box has a surface area of 2(12.5*19.5+12.5*26+19.5*26)=2151.5sq cm. If packed in two levels the surface area of 2(25*19.5+25*13+19.5*13)=2132sq cm. So the double layer packing uses less material.