Transcript Slide 1

Scaling Three-Dimensional
Figures
7.9
Pre-Algebra
Warm Up
Find the surface area of each rectangular
prism.
1. length 14 cm, width 7 cm, height 7 cm 490 cm2
2. length 30 in., width 6 in., height 21 in 1872 in2
3. length 3 mm, width 6 mm, height 4 mm 108 mm2
4. length 37 in., width 9 in., height 18 in.
2322 in2
Learn to make scale models of solid figures.
Vocabulary
capacity
Calculations
Capacity
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.
Helpful Hint
Multiplying the linear dimensions of a solid by n
creates n2 as much surface area and n3 as much
volume.
Example: 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.
Example: 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.
Example: 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.
Try This
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.
Try This
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.
Try This
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.
Example: 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.
Example: 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.
Try This
A box is in the shape of a rectangular prism.
The box is 8 ft tall, and its base has a length of
6 ft and a width of 4 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
8 ft
96 in. 16
Convert and simplify.
The scale factor of the model is 1:16.
Try This
B. What are the length and the width of the
model?
1  6 ft = 72 in. = 41 in.
Length: 16
16
2
Width: 1 4 ft = 48 in. = 3 in.
16
16
The length of the model is 4 1
2 in., and the width is
3 in.
Example: 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
V = 2 ft
30

2 ft

8=x
Multiply.
240 = x
Calculate the fill time.
It takes 240 seconds, or 4 minutes, to fill the larger
container.

Try This
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.

Lesson Quiz: Part 1
A 10 cm cube is built from small cubes, each 1
cm on an edge. Compare the following values.
1. the edge lengths of the two cubes 10:1
2. the surface areas of the two cubes 100:1
3. the volumes of the two cubes 1000:1
Lesson Quiz: Part 2
4. A pyramid has a square base measuring
185 m on each side and a height of 115 m.
A model of it has a base 37 cm on each
side. What is the height of the model?
23 cm
5. A cement truck is pouring cement for a new
4 in. thick driveway. The driveway is 90 ft
long and 20 ft wide. How long will it take
the truck to pour the cement if it releases
10 ft3 of cement per minute?
60 min