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Pre-Algebra
7-8 Scale Models7-8 Scale Models
Pre-Algebra
Warm UpWarm Up
Problem of the DayProblem of the Day
Lesson PresentationLesson Presentation
Pre-Algebra
7-8 Scale Models
Warm UpThe scale of a drawing is 4 in. = 12 ft. Find each actual measurement.
1. 6 in. 2. 2.5 in.
The scale of a map is 1 in. = 3.5 mi. Find each length on the map.
3. 21 mi 4. 1.75 mi
18 ft 7.5 ft
6 in.
Pre-Algebra
7-8 Scale Models
0.5 in.
Pre-Algebra
7-8 Scale Models
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
Pre-Algebra
7-8 Scale Models
Learn to make comparisons between and find dimensions of scale models and actual objects.
Pre-Algebra
7-8 Scale Models
Vocabulary
scale model
Pre-Algebra
7-8 Scale Models
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.
Pre-Algebra
7-8 Scale Models
Tell whether each scale reduces, enlarges, or preserves the size of the actual object.
A. 1 in:1 yd
Additional Example 1A: Analyzing and Classifying Scale Factors
1 in.1 yd
= 1 in.36 in.
= Convert: 1 yd = 36 in. Simplify.
The scale reduces the size of the actual object by a
factor of . 136
136
Pre-Algebra
7-8 Scale Models
Tell whether each scale reduces, enlarges, or preserves the size of the actual object.
B. 1 m:10 cm
Additional Example 1B: Analyzing and Classifying Scale Factors
= 100 cm10 cm
= 10 Convert: 1 m = 100 cm. Simplify.
The scale enlarges the size of the actual object 10 times.
1 m10 cm
Pre-Algebra
7-8 Scale Models
Tell whether each scale reduces, enlarges, or preserves the size of the actual object.
A. 1 in:1 ft
Try This: Example 1A
1 in.1 ft
= 1 in.12 in.
= Convert: 1 ft = 12 in. Simplify.
The scale reduces the size of the actual object by a
factor of . 112
112
Pre-Algebra
7-8 Scale Models
Tell whether each scale reduces, enlarges, or preserves the size of the actual object.
B. 12 in:1 ft
Try This: Example 1B
12 in. 1 ft
= 1 ft1 ft
= 1 Convert: 12 in. = 1 ft. Simplify.
The scale preserves the size of the actual object.
Pre-Algebra
7-8 Scale Models
What scale factor relates a 12 in. scale model to a 6 ft. man?
Additional Example 2: Finding Scale Factors
12 in 6 ft
= 12 in.72 in.
= Write the scale factor as a ratio and simplify.
12 in:6 ft State the scale.
16
The scale factor is , or 1:6. 16
Pre-Algebra
7-8 Scale Models
What scale factor relates a 12 in. scale model to a 4 ft. tree?
Try This: Example 2
12 in 4 ft
= 12 in.48 in.
= Write the scale factor as a ratio and simplify.
12 in:4 ft State the scale.
14
The scale factor is , or 1:4. 14
Pre-Algebra
7-8 Scale Models
A model of 32 ft tall house was made using the scale 3 in:2 ft. What is the height of the model?
Additional Example 3: Finding Unknown Dimensions Given Scale Factors
First find the scale factor.
The scale factor for the model is . Now set up a proportion.
18
3 in.2 ft
= 3 in.24 in.
= 1 in.8 in.
= 18
384 = 8h
Convert: 32 ft = 384 in.
Cross multiply.
48 = h
The height of the model is 48 in.Solve for the height.
18
= h in.384 in.
Pre-Algebra
7-8 Scale Models
A model of 24 ft tall bridge was made using the scale 4 in:2 ft. What is the height of the model?
Try This: Example 3
First find the scale factor.
The scale factor for the model is . Now set up a proportion.
16
4 in.2 ft
= 4 in.24 in.
= 1 in.6 in.
= 16
288 = 6h
Convert: 24 ft = 288 in.
Cross multiply.
48 = h
The height of the model is 48 in.Solve for the height.
16
= h in.288 in.
Pre-Algebra
7-8 Scale Models
A DNA model was built using the scale 5 cm: 0.0000001 mm. If the model of the DNA chain is 20 cm long, what is the length of the actual chain? Find the scale factor.
Additional Example 4: Life Science Application
The scale factor for the model is 500,000,000. This means the model is 500 million times larger than the actual chain.
5 cm 0.0000001 mm
50 mm 0.0000001 mm= = 500,000,000
Pre-Algebra
7-8 Scale Models
Additional Example 4 Continued
500,000,000 1
20 cm x cm= Set up a proportion.
500,000,000x = 1(20)
x = 0.00000004
The length of the DNA chain is 4 10-8 cm.
Cross multiply.
Solve for the length.
Pre-Algebra
7-8 Scale Models
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.
Try This: Example 4
The scale factor for the model is 2,000. This means the actual object is 2 thousand times larger than the model.
2 cm 0.01 mm
20 mm 0.01 mm= = 2,000
Pre-Algebra
7-8 Scale Models
Try This: Example 4 Continued
2,000 1
30 cm x cm= Set up a proportion.
2,000x = 1(30)
x = 0.015
The length of the actual object is 0.015 cm.
Cross multiply.
Solve for the length.
Pre-Algebra
7-8 Scale Models
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
3. 400 m:1 km
4. What scale factor was used to build a 5 in.
model of a 60 ft statue?
Pre-Algebra
7-8 Scale Models
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?
