MMM Project - Designing Packages, teacher pages 7

Extensions
12.	Many brands of soft drink are packaged in rectangular boxes of 24 cans.
	a.	During the spring of 1993, a major cola company announced that they were going to package 24 cans into a more cube-like shape. Why might the company have done this?
	b.	List all the ways 24 cans of soda could be arranged and packaged in a rectangular box. Which arrangement would you recommend that a soft drink company use? Why?
13.	Slam Dunk Sporting Goods packages its basketballs in cubic boxes with 1-ft edges:
	a.	Slam Dunk ships basketballs from its factory to stores all over the country. To ship the balls, the company packs 12 basketballs (in their boxes) into a large rectangular shipping box. Find the dimensions of every possible shipping box into which the boxes of balls would exactly fit.
	b.	Find the surface area of each shipping box you found in part a.
	c.	Slam Dunk uses the shipping box that requires the least material. Which shipping box do they use?
	d.	Slam Dunk decides to ship basketballs in boxes of 24. They want to use the shipping box that requires the least material. Find the dimensions of the box they should use. How much more packaging material is needed to ship 24 balls than to ship 12 balls?

Answers

Extensions

12a. A cube-like shape requires less packaging material. The company may have been responding to environmental concerns of consumers. They may also have wanted to change their packaging to get consumers' attention.

12b. The possible arrangements are 1 by 1 by 24, 1 by 2 by 12, 1 by 3 by 8, 1 by 4 by 6, 2 by 2 by 6, 2 by 3 by 4; dimensions may be width, depth or height of the box. Possible recommendation: The 1 by 1 by 24 looks like more product but would be quite difficult to carry; the 2 by 2 by 6 may be the easiest to carry.

13a. 1 by 1 by 12, 1 by 2 by 6, 1 by 3 by 4, and 2 by 2 by 3.

13b. The surface areas of the boxes above are 50 ft², 40 ft², 38 ft², and 32 ft².

13c. the 2 by 2 by 3 box.

13d. Any of the arrangements shown above with one of its dimensions doubled will result in a box that would hold 24 basketballs. The one that uses the least amount of material is a 2 by 3 by 4 box, requiring 52 ft² of material, 20 ft² more than the box that requires the least amount of material to hold 12 basketballs.