Spatial Reasoning using Cubes and Isometric Drawings
Part Four -- Volume & Surface Area

 

The volume of a solid is the number of unit cubes that fit inside.

The surface area of a solid is the number of square faces that show on the outside.

For example, the volume of the following figure is 4 unit cubes, and its surface area is 18 unit squares.

.

The SEPARATE FACES tool disconnects the faces of the cube so that they can be moved around or colored separately. Click on this tool and verify that the surface area of this figure is 18.

Activity 1: Finding Patterns

Task 1

1. Look at each drawing below. Click on the figure to use the drawing tool.

What is the volume of each figure?
What is the surface area of each figure?

A. B. C.

2. What conjectures or statements can you make about the surface area of a figure built using 7 cubes?

Task 2

Use the drawing tool to help you fill out the table below.

The first column lists a number of cubes you should use to build a figure (one to six).
In the second column, list the possible volume(s) of a solid built with that number of cubes.
In the third column, list the possible surface area(s) of a solid built with that number of cubes.

 
# of cubes
Volume(s)
Surface Area(s)
One    
Two    
Three    
Four    
Five    
Six    

Reflections:

1. What pattern(s) did you notice about the volumes?

2. What pattern(s) did you notice about the maximum surface areas? the minimum surface areas?

3. What do you notice about the list of surface areas for a fixed number of cubes?

Do you think that this is always true for isometric drawings?
Give a justification for your answer.

Click here to return to the beginning of the investigation.

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Last updated: April 3, 2002

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