7-9 Scaling Three-Dimensional Figures
Learn to make scale models of solid
figures.
Pre-Algebra
7-9 Scaling Three-Dimensional Figures
Pre-Algebra
7-9 Scaling Three-Dimensional Figures
Helpful Hint
Multiplying the linear dimensions of a solid by n
creates n2 as much surface area and n3 as much
volume.
Pre-Algebra
7-9 Scaling Three-Dimensional Figures
Example 1A: Scaling Models That Are Cubes
A 3 cm cube is built from small cubes, each 1
cm on an edge. Compare the following values.
A. the edge lengths of the large and small
cubes
3 cm cube
1 cm cube
3 cm = 3 Ratio of corresponding
1 cm
edges
The edges of the large cube are 3 times as long as
the edges of the small cube.
Pre-Algebra
7-9 Scaling Three-Dimensional Figures
Example 1B: Scaling Models That Are Cubes
B. the surface areas of the two cubes
3 cm cube
1 cm cube
54 cm2 = 9 Ratio of corresponding
areas
6 cm2
The surface area of the large cube is 9 times that
of the small cube.
Pre-Algebra
7-9 Scaling Three-Dimensional Figures
Example 1C: Scaling Models That Are Cubes
C. the volumes of the two cubes
3 cm cube
1 cm cube
27 cm3 = 27 Ratio of corresponding
volumes
1 cm3
The volume of the large cube is 27 times that of
the small cube.
Pre-Algebra
7-9 Scaling Three-Dimensional Figures
Pre-Algebra
7-9 Scaling Three-Dimensional Figures
Corresponding edge lengths of any two cubes
are in proportion to each other because the
cubes are similar. However, volumes and
surface areas do not have the same scale
factor as edge lengths.
Each edge of the 2 ft cube is 2 times as long as
each edge of the 1 ft cube. However, the
cube’s volume, or capacity, is 8 times as
large, and its surface area is 4 times as large
as the 1 ft cube’s.
Pre-Algebra
7-9 Scaling Three-Dimensional Figures
Example 2: Scaling Models That Are Other Solid
Figures
A box is in the shape of a rectangular prism.
The box is 4 ft tall, and its base has a length of
3 ft and a width of 2 ft. For a 6 in. tall model of
the box, find the following.
A. What is the scale factor of the model?
6 in. = 6 in. = 1
4 ft
48 in. 8
Convert and simplify.
The scale factor of the model is 1:8.
Pre-Algebra
7-9 Scaling Three-Dimensional Figures
Example 2B: Scaling Models That Are Other Solid
Figures
B. What are the length and the width of the
model?
 3 ft = 36 in. = 41 in.
Length: 1
8
8
2
 2 ft = 24 in. = 3 in.
Width: 1
8
8
The length of the model is 4 1
2 in., and the width is
3 in.
Pre-Algebra
7-9 Scaling Three-Dimensional Figures
Example 3: Business Application
It takes 30 seconds for a pump to fill a cubic
container whose edge measures 1 ft. How long
does it take for the pump to fill a cubic
container whose edge measures 2 ft?
2 ft = 8 ft3 Find the volume of the
2 ft cubic container.
Set up a proportion and solve.
30 s = x
Cancel units.
3
3
1 ft
8 ft
30  8 = x
Multiply.
V = 2 ft

2 ft

240 = x
Calculate the fill time.
It takes 240 seconds, or 4 minutes, to fill the larger
container.
Pre-Algebra
7-9 Scaling Three-Dimensional Figures
Try This: Example 3
It takes 30 seconds for a pump to fill a cubic
container whose edge measures 1 ft. How long
does it take for the pump to fill a cubic
container whose edge measures 3 ft?
V = 3 ft  3 ft  3 ft = 27 ft3 Find the volume of the
2 ft cubic container.
Set up a proportion and solve.
30 s = x
1 ft3 27 ft3
30  27 = x
Multiply.
810 = x
Calculate the fill time.
It takes 810 seconds, or 13.5 minutes, to fill the larger
container.
Pre-Algebra
7-9 Scaling Three-Dimensional Figures
Pre-Algebra
7-9 Scaling Three-Dimensional Figures
Try This: Example 1A
A 2 cm cube is built from small cubes, each 1
cm on an edge. Compare the following values.
A. the edge lengths of the large and small
cubes
2 cm cube
1 cm cube
2 cm = 2 Ratio of corresponding
1 cm
edges
The edges of the large cube are 2 times as long as
the edges of the small cube.
Pre-Algebra
7-9 Scaling Three-Dimensional Figures
Try This: Example 1B
B. the surface areas of the two cubes
2 cm cube
1 cm cube
24 cm2 = 4 Ratio of corresponding
areas
6 cm2
The surface area of the large cube is 4 times that
of the small cube.
Pre-Algebra
7-9 Scaling Three-Dimensional Figures
Try This: Example 1C
C. the volumes of the two cubes
2 cm cube
1 cm cube
8 cm3 = 8 Ratio of corresponding
volumes
1 cm3
The volume of the large cube is 8 times that of the
small cube.
Pre-Algebra
7-9 Scaling Three-Dimensional Figures
Corresponding edge lengths of any two cubes
are in proportion to each other because the
cubes are similar. However, volumes and
surface areas do not have the same scale
factor as edge lengths.
Each edge of the 2 ft cube is 2 times as long as
each edge of the 1 ft cube. However, the
cube’s volume, or capacity, is 8 times as
large, and its surface area is 4 times as large
as the 1 ft cube’s.
Pre-Algebra