Question

12 cans of soup each can is a cylinder with a radius of 3.5 cm and a height of 10 cm. the cans may be arranged in any way. the company would like to minimize the packaging costs involved with the creation of the container.

Answer 1

2 layers, 3×2 cans per layer

Explanation:

Factors of 12: 1, 2, 3, 4, 6, 12

The box can have 1 layer of 12 cans, 2 layers of 6 cans each, or 3 layers of 4 cans each.

In each case below, the total surface area is 2(LW + LH + WH)

1 layer, 12×1 cans

L = 84 cm; W = 7 cm; H = 10 cm

SA = 2996 cm²

1 layer, 6×2 cans

L = 42 cm; W = 14 cm; H = 10 cm

SA = 2248 cm²

1 layer, 4×3 cans

L = 28 cm; W = 21 cm; H = 10 cm

SA = 2156 cm²

2 layers, 6×1 cans per layer

L = 42 cm; W = 7 cm; H = 20 cm

SA = 2548 cm²

2 layers, 3×2 cans per layer

L = 21 cm; W = 14 cm; H = 20 cm

SA = 1988 cm² <--------------- smallest surface area

3 layer, 4×1 cans per layer

L = 28 cm; W = 7 cm; H = 30 cm

SA = 2492 cm²

3 layers, 2×2 cans per layer

L = 14 cm; W = 14 cm; H = 30 cm

SA = 2072 cm²