Scale Drawings and Scale Models
Learn to understand ratios and
proportions in scale drawings. Learn to
use ratios and proportions with scale.
Course 2
InsertDrawings
Lesson Title
Scale
andHere
Scale Models
Vocabulary
scale model
scale factor
scale
scale drawing
Course 2
Scale Models and Scale Drawings
This HO gauge model train is a
scale model of a historic train. A
scale model is a proportional
model of a three-dimensional
object. Its dimensions are related
to the dimensions of the actual
object by a ratio called the scale
factor. The scale factor of an HO
1
gauge model train is 87 .
1
This means that each dimension of the model is
87
of the corresponding dimension of the actual train.
Course 2
Scale Models and Scale Drawings
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 drawing is a proportional drawing of an
object. Both scale drawings and scale models
can be smaller or larger than the objects they
represent.
Course 2
Scale Drawings and Scale Models
Example 1: Finding a Scale Factor
Identify the scale factor.
Room
Blueprint
Length (in.)
144
18
Width (in.)
108
13.5
blueprint length = 18
144
room length
= 1
8
The scale factor is 1 .
8
Course 2
Write a ratio using one of the
dimensions.
Simplify.
Insert
Lesson Title
Scale Drawings
andHere
Scale Models
Try This: Example 2
Identify the scale factor.
Model Aircraft
Blueprint
Length (in.)
12
2
Wing span (in.)
18
3
blueprint length = 2
aircraft length
12
= 1
6
The scale factor is 1 .
6
Course 2
Write a ratio using one of
the dimensions.
Simplify.
Scale Drawings and Scale Models
Example 3: Using Scale Factors to Find Unknown
Lengths
A photograph was enlarged and made into a poster.
The poster is 20.5 inches by 36 inches. The scale
5
factor is 1 . Find the size of the photograph.
poster = 5
Think:
photo
1
36 = 5
l
1
5l = 36
l = 7.2
Course 2
Write a proportion to find the
length l.
What times 5 is 36?
Scale Drawings and Scale Models
Example 3 Continued
A photograph was enlarged and made into a poster.
The poster is 20.5 inches by 36 inches. The scale
5
factor is 1 . Find the size of the photograph.
poster = 5
Think:
photo
1
20.5 = 5
w
1
Write a proportion to find the
width w.
5w = 20.5 What times 5 is 20.5?
w = 4.1
The photo is 7.2 in. long and 4.1 in. wide.
Course 2
Scale Drawings and Scale Models
Try This: Example 4
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 1.5. Find the size of the dollhouse.
1
Think:
dollhouse = 1.5
blueprint
1
l = 1.5
45
1
1(45) = 45
l = 45 · 1.5
l = 67.5
Course 2
Write a proportion to
find the length l.
What times 1 is 45?
Multiply 1.5 by 45.
Scale Drawings and Scale Models
Example 4 Continued
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 1.5. Find the size of the dollhouse.
1
Think:
dollhouse =
blueprint
w =
24
1.5
1
1.5
1
Write a proportion
to find the width w.
What times 1 is 24?
1(24) = 24
w = 24 · 1.5 Multiply 1.5 by 24.
w = 36
The dollhouse is 67.5 inches long and 36 inches wide.
Course 2
Scale Drawings and Scale Models
Example 5: Measurement Application
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?
Let d be the actual distance between the cities.
1.5 = 7.5
Write a proportion.
60
d
1.5(5) = 7.5
60(5) = ?
What times 1.5 equals 7.5?
Multiply 60 by 5.
d = 300
The distance between the cities is 300 miles.
Course 2
5-7 Insert
Lesson Title
Scale Drawings
andHere
Scale Models
Try This: Example 6
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= 7
Write a proportion.
50 d
1(7) = 7
What times 1 equals 7?
50(7) = ?
Multiply 50 by 7
d = 350
The distance between the cities is 350 kilometers.
Course 2
Scale
InsertDrawings
Lesson Title
andHere
Scale Models
Show all work on recording sheet.
Identify the scale factor.
1.
Height (in.)
Statue of Liberty
Model
1,824
8
1
228
2. On a scale drawing, a kitchen wall is 6 inches long.
1
The scale factor is
. What is the length of the
24
actual wall?
144 inches, or 12 feet
Course 2
5-7 Scale
InsertDrawings
Lesson Title
andHere
Scale Models
Show all work on recording sheet.
3. On a road map, the distance from Green Bay to
Chicago is 11 cm. What is the actual distance
between the cities if the map scale is 3 cm = 90 km?
330 km
Course 2