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4-6 Scale Drawings and Scale Models
Warm UpWarm Up
Lesson PresentationLesson Presentation
Problem of the DayProblem of the Day
Lesson QuizzesLesson Quizzes
4-6 Scale Drawings and Scale Models
Warm UpWrite each fraction in the simplest form.
1. 4
482. 9
135
Convert the following measurements.
3. 192 inches = feet
4. 18.5 feet = inches
5. 324 inches = feet
16
222
27
112
115
4-6 Scale Drawings and Scale Models
Problem of the Day
A toy model of a 200 foot dinosaur is 3 in. long. How many times as long as the model is the dinosaur? 800
4-6 Scale Drawings and Scale Models
Learn to understand ratios and proportions in scale drawings. Learn to use ratios and proportions with scale.
4-6 Scale Drawings and Scale Models
Vocabulary
scale drawing
scale factorscale modelscale
4-6 Scale Drawings and Scale Models
A scale drawing is a proportional two-dimensional drawing of an object.
Its dimensions are related to the dimensions of the actual object by a ratio called the scale factor. For example, if a drawing of a building has
a scale factor of , this means that each
dimension of the drawing is of the
corresponding dimension of the actual building.
187
187
4-6 Scale Drawings and Scale Models
A scale is the ratio between two sets of measurements. Scales can use the same units or different units. The photograph shows a scale drawing of the model train.
A scale model is a proportional three- dimensional model of an object.
4-6 Scale Drawings and Scale Models
Identify the scale factor.
Additional Example 1: Finding a Scale Factor
13.5108Width (in.)
18144Length (in.)
BlueprintRoom
blueprint lengthroom length
= 18
18
The scale factor is .
Write a ratio using one of thedimensions.
Simplify.
18144
=
A scale factor is always the ratio of the model’s dimensions to the actual object’s dimensions.
Caution!
4-6 Scale Drawings and Scale Models
Check It Out: Example 1
Identify the scale factor.
318Wing span (in.)
212Length (in.)
BlueprintModel Aircraft
blueprint length aircraft length
= 212
= 16
Write a ratio using one of the dimensions.
Simplify.
The scale factor is . This is reasonable because of the length of the model is 3 in. The length of the blueprint is 2, which is less. is less than .
16
14
16
14
4-6 Scale Drawings and Scale Models
A photograph was enlarged and made into a poster. The poster is 20.5 inches by 36 inches.
The scale factor is . Find the size of the photograph.
Additional Example 2: Using Scale Factors to Find Unknown Lengths
51
Think: posterphoto
= 51
36 l
= 51
5l = 36
l = 7.2
Write a proportion to find the length l.
Find the cross products.
Divide.
4-6 Scale Drawings and Scale Models
A photograph was enlarged and made into a poster. The poster is 20.5 inches by 36 inches.
The scale factor is . Find the size of the photograph.
Additional Example 2 Continued
51
Think: posterphoto
= 51
20.5 w
= 51
5w = 20.5
w = 4.1
Write a proportion to find the width w.
Find the cross products.
Divide.
The photo is 7.2 in. long and 4.1 in. wide.
4-6 Scale Drawings and Scale Models
Check It Out: Example 2
Mary’s father made her a dollhouse which was modeled after the blueprint of their home. The blueprint is 24 inches by 45 inches. The scale
factor is . Find the size of the dollhouse. 1.51
Think: dollhouseblueprint
= 1.51
l = 45 · 1.5
l = 67.5
Write a proportion to find the length l.
Find the cross products.
Multiply.
l 45
= 1.51
4-6 Scale Drawings and Scale Models
Check It Out: Example 2 Continued
w 24
= 1.51
w = 24 · 1.5
w = 36
Write a proportion to find the width w.
Find the cross products.
Multiply.The dollhouse is 67.5 inches long and 36 inches wide.
Think: dollhouseblueprint
= 1.51
Mary’s father made her a dollhouse which was modeled after the blueprint of their home. The blueprint is 24 inches by 45 inches. The scale
factor is . Find the size of the dollhouse. 1.51
4-6 Scale Drawings and Scale Models
On a road map, the distance between Pittsburgh and Philadelphia is 7.5 inches. What is the actual distance between the cities if the map scale is 1.5 inches = 60 miles?
Additional Example 3: Measurement Application
Let d be the actual distance between the cities.
1.560
= 7.5d
1.5 · d = 60 · 7.5
1.5d = 4501.5d1.5
= 4501.5
d = 300The distance between the cities is 300 miles.
Write a proportion.
Find the cross products.
Multiply.
Divide both sides by 1.5.
4-6 Scale Drawings and Scale Models
Check It Out: Example 3
On a road map, the distance between Dallas and Houston is 7 inches. What is the actual distance between the cities if the map scale is 1 inch = 50 kilometers?
Let d be the actual distance between the cities.1
50= 7
d
1 · d = 50 · 7
1d = 350
d = 350
The distance between the cities is 350 kilometers.
Write a proportion.
Find the cross products.
Multiply.
4-6 Scale Drawings and Scale Models
Standard Lesson Quiz
Lesson Quizzes
Lesson Quiz for Student Response Systems
4-6 Scale Drawings and Scale Models
Lesson Quiz: Part I
Identify the scale factor.
81,824Height (in.)
ModelStatue of Liberty1.
2.
144 inches, or 12 feet
1228
On a scale drawing, a kitchen wall is 6 inches long.
The scale factor is . What is the length of the
actual wall?
124
4-6 Scale Drawings and Scale Models
Lesson Quiz: Part II
3. On a road map, the distance from Green Bay toChicago is 11 cm. What is the actual distance between the cities if the map scale is 3 cm = 90 km?
330 km
4-6 Scale Drawings and Scale Models
1. Identify the scale factor.
A. C. 10
B. D. 20
Lesson Quiz for Student Response Systems
1 20
1 10
Fish Model
Length (cm) 120 12
4-6 Scale Drawings and Scale Models
2. On a scale drawing, the height of a building
is 60 inches. The scale factor is . What is
the height of the actual building?
A. 240 in., or 20 ft
B. 300 in., or 25 ft
C. 600 in., or 50 ft
D. 900 in., or 75 ft
Lesson Quiz for Student Response Systems
1 15
4-6 Scale Drawings and Scale Models
3. On a road map, the distance from Washington, DC to New York is 15 cm. What is the actual distance between the cities if the map scale is 3 cm = 50 mi?
A. 150 mi
B. 200 mi
C. 250 mi
D. 300 mi
Lesson Quiz for Student Response Systems
