Scale Drawings and
Scale Models
Vocabulary
scale drawing: proportional two-dimensional drawing of an object (smaller or larger)
scale model: proportional three-dimensional model of an object (smaller or larger)
scale factor: a ratio of the model/drawing’s dimensions to the actual object’s dimensions in
simplest form
scale: ratio between two sets of measurements
Examples of Scale Drawings
blueprints
maps
Examples of Scale Models
toy car
model of a house
toy airplane
Finding Scale Factor
model’s dimensions
actual object’s dimensions
Caution!!!
A scale factor is ALWAYS the
ratio of the model’s
dimensions to the actual
object’s dimensions.
Caution!!
It’s alright to have a scale factor
greater than 1. If the scale factor is
greater than 1, this means that the
new figure is bigger than the original
(think about cells). If the scale factor is
less than 1, then the new figure is
smaller than the original (think about
model airplanes).
Finding a Scale Factor
You can use the lengths or heights to find the scale factor.
Airplane
Model
MODEL LENGTH
20
AIRPLANE LENGTH 1,800
THEN SIMPLIFY!
Length
(in.)
1,800
Height
(in.)
756
20
8.4
20 ÷ 20
1
=
1,800 ÷ 20
90
SCALE
FACTOR!
Finding a Scale Factor
You can use the lengths or heights to find the scale factor.
Airplane
Model
MODEL HEIGHT
AIRPLANE HEIGHT
THEN SIMPLIFY!
Length
(in.)
1,800
Height
(in.)
756
20
8.4
8.4 ÷ 8.4
1
=
756 ÷ 8.4
90
SCALE
FACTOR!
8.4
756
Finding a Scale Factor
Height
(in.)
Great
Dane
Model
35
10
MODEL HEIGHT
GREAT DANE HEIGHT
THEN SIMPLIFY!
10
35
÷5
÷5
SCALE
FACTOR!
=
2
7
10
35
Using Scale
On a road map with a scale of 1 cm: 120 mi., the
distance between two cities measures 3.5 cm.
What is the actual distance between these two
cities?
MODEL
1 cm
=
ACTUAL
120 mi
3.5 cm
x mi
420 ÷ 1 = 420
The actual distance between these two cities is 420 miles.
Using Scale
Jeffery is making a model of a car. He uses the
scale 1 in:12 in. If the length of the actual car is
132 in., what is the length of his model car?
MODEL
1 in
x in
=
ACTUAL
12 in
132 in
132 ÷ 12 = 11
The length of his model car is 11 in.
Using Scale Factor
Kelly enlarged her favorite photograph into a
poster. The poster is 22 inches by 38 inches. The
scale factor is 6/1. Find the size of the original
photograph. Round to the nearest tenth.
22 inches
x inches
x inches
38 inches
Using Scale Factor
Kelly enlarged her favorite photograph into a poster. The
poster is 22 inches by 38 inches. The scale factor is 6/1. Find
the size of the original photograph. Round to the nearest
tenth.
Let’s find length first!
MODEL
6 in
38 in
=
ACTUAL
1 in
x in
38 ÷ 6 = 6.3
Using Scale Factor
Kelly enlarged her favorite photograph into a
poster. The poster is 22 inches by 38 inches. The
scale factor is 6/1. Find the size of the original
photograph. Round to the nearest tenth.
22 inches
x inches
6.3 inches
38 inches
Using Scale Factor
Kelly enlarged her favorite photograph into a poster. The
poster is 22 inches by 38 inches. The scale factor is 6/1. Find
the size of the original photograph. Round to the nearest
tenth.
Now let’s find the width!
MODEL
6 in
ACTUAL
1 in
=
22 in
x in
22 ÷ 6 = 3.6
Using Scale Factor
Kelly enlarged her favorite photograph into a
poster. The poster is 22 inches by 38 inches. The
scale factor is 6/1. Find the size of the original
photograph. Round to the nearest tenth.
3.6 inches
6.3 inches
22 inches
38 inches
Now we know...
The original size of the photograph
is 3.6 inches by 6.3 inches.
In this case, the scale factor was
larger than one. This means, that
the model is larger than the
original.
Try This:
On a scale drawing of a horse, the scale is
1 mm: 10 mm. If the real horse is 1,500 mm
tall, how tall is the horse on the scale
drawing?