1. 7-8 Scale Models Warm Up Problem of the Day Lesson Presentation
Pre-Algebra

2. Pre-Algebra
7-8
Scale Models
Warm Up
The scale of a drawing is 4 in. = 12 ft. Find each actual measurement.
1. 6 in in.
The scale of a map is 1 in. = 3.5 mi. Find each length on the map.
3. 21 mi mi
18 ft
7.5 ft
6 in.
0.5 in.

3. Problem of the Day
There is a 2.5-mile racetrack at the Indianapolis Motor Speedway. If a drawing of the racetrack has a scale of 1:1760, what is the length of the track on the drawing?
7.5 ft

4. Learn to make comparisons between and find dimensions of scale models and actual objects.

5. Vocabulary
scale model

6. Very large and very small objects are often modeled
Very large and very small objects are often modeled. A scale model is a three-dimensional model that accurately represents a solid object. The scale model is mathematically similar to the solid object.
A scale gives the ratio of the dimensions of the model to the actual dimensions.

7. Additional Example 1A: Analyzing and Classifying Scale Factors
Tell whether each scale reduces, enlarges, or preserves the size of the actual object.
A. 1 in:1 yd
1 in.
1 yd
1 in.
36 in. 1 36 = =
Convert: 1 yd = 36 in. Simplify.
The scale reduces the size of the actual object by a factor of . 1 36

8. Additional Example 1B: Analyzing and Classifying Scale Factors
Tell whether each scale reduces, enlarges, or preserves the size of the actual object.
B. 1 m:10 cm
1 m
10 cm
100 cm
10 cm
Convert: 1 m = 100 cm. Simplify. =
= 10
The scale enlarges the size of the actual object 10 times.

9. Try This: Example 1A
Tell whether each scale reduces, enlarges, or preserves the size of the actual object.
A. 1 in:1 ft
1 in.
1 ft
1 in.
12 in. 1 12
Convert: 1 ft = 12 in. Simplify. = =
The scale reduces the size of the actual object by a factor of . 1 12

10. Try This: Example 1B
Tell whether each scale reduces, enlarges, or preserves the size of the actual object.
B. 12 in:1 ft
12 in.
1 ft
1 ft =
= 1
Convert: 12 in. = 1 ft. Simplify.
The scale preserves the size of the actual object.

11. Additional Example 2: Finding Scale Factors
What scale factor relates a 12 in. scale model to a 6 ft. man?
12 in:6 ft State the scale.
12 in
6 ft
12 in.
72 in. 1 6
Write the scale factor as a ratio and simplify. = =
The scale factor is , or 1:6. 1 6

12. Try This: Example 2
What scale factor relates a 12 in. scale model to a 4 ft. tree?
12 in:4 ft State the scale.
12 in
4 ft
12 in.
48 in. 1 4
Write the scale factor as a ratio and simplify. = =
The scale factor is , or 1:4. 1 4

13. Additional Example 3: Finding Unknown Dimensions Given Scale Factors
A model of 32 ft tall house was made using the scale 3 in:2 ft. What is the height of the model?
3 in.
2 ft =
3 in.
24 in. =
1 in.
8 in. 1 8 =
First find the scale factor.
The scale factor for the model is . Now set up a proportion. 1 8 1 8 =
h in.
384 in.
Convert: 32 ft = 384 in.
384 = 8h
Cross multiply.
48 = h
Solve for the height.
The height of the model is 48 in.

14. Try This: Example 3
A model of 24 ft tall bridge was made using the scale 4 in:2 ft. What is the height of the model?
4 in.
2 ft =
4 in.
24 in. =
1 in.
6 in. 1 6 =
First find the scale factor.
The scale factor for the model is . Now set up a proportion. 1 6 1 6 =
h in.
288 in.
Convert: 24 ft = 288 in.
288 = 6h
Cross multiply.
48 = h
Solve for the height.
The height of the model is 48 in.

15. Additional Example 4: Life Science Application
A DNA model was built using the scale 5 cm: mm. If the model of the DNA chain is 20 cm long, what is the length of the actual chain? Find the scale factor.
5 cm mm
50 mm =
= 500,000,000
The scale factor for the model is 500,000,000. This means the model is 500 million times larger than the actual chain.

16. Additional Example 4 Continued
500,000,000 1
20 cm
x cm =
Set up a proportion.
500,000,000x = 1(20)
Cross multiply.
x =
Solve for the length.
The length of the DNA chain is 4  10-8 cm.

17. Try This: Example 4
A model was built using the scale 2 cm:0.01 mm. If the model is 30 cm long, what is the length of the actual object? Find the scale factor.
2 cm
0.01 mm
20 mm =
= 2,000
The scale factor for the model is 2,000. This means the actual object is 2 thousand times larger than the model.

18. Try This: Example 4 Continued
2,000 1
30 cm
x cm =
Set up a proportion.
2,000x = 1(30)
Cross multiply.
Solve for the length.
x = 0.015
The length of the actual object is cm.

19. Lesson Quiz: Part 1
Tell whether each scale reduces, enlarges, or preserves the size of the actual object.
1. 75 ft:40 in
2. 1 mi:1760 yd
m:1 km
4. What scale factor was used to build a 5 in. model of a 60 ft statue?
enlarges
preserves
reduces
1:144

20. Lesson Quiz: Part 2
5. To create a model of the Eustachian tube of the human ear, an audiologist used the scale 1.5 cm = 0.6 mm. If the diameter of the Eustachian tube is 1.8 mm, what is the diameter of the model?
4.5 cm