Investigation 2 Packaging Blocks
Problem 1 Finding Surface Area
Date:
My Goals for this Problem are to connect the dimensions of a rectangular prism to its volume and
surface area and to understand that rectangular prisms may have the same volume but quite
different surface areas.
ATC Toy Company is planning to market a set of children’s alphabet blocks.
Each block is a cube with 1-inch edges, so each block as a volume of 1 cubic inch.
The company wants to arrange 24 blocks in the shape of a rectangular prism and
then package them in a box that exactly fits the prism.
A. Find all the ways 24 cubes can be arranged into a rectangular prism.
Possible Arrangements of 24 Cubes
Length
(in.)
Width
(in.)
Height
(in.)
Volume
(in.3)
Surface
Area (in. 2)
1
1
24
24
98
1
2
12
24
76
1
3
8
24
70
1
4
6
24
68
2
2
6
24
56
2
3
4
24
52
Sketch
B. Which of your arrangements requires the box made with the least material?
Which requires the box made with the most material?
C. Which arrangement would you recommend to ATC Toy Company? Explain why.
D. Why do you think the company makes 24 alphabet blocks rather than 26?
Things I noticed and want to remember:
Questions I still have:
Summary: