Chapter 6 Lesson 3
Scale Drawings & Models
pgs. 276-280
What you will learn:
Use scale drawings
Construct scale drawings
Vocabulary
• Scale drawing/scale model (276): is
used to represent an object that is
too large or too small to be drawn
or built at actual sizes
• Scale (276): gives the relationship between
the measurements on the drawing or
model and the measurements of the real
object
• Scale factor (277): the ratio of a length on a
scale drawing or model to the
corresponding length on the real object
Scale
Example:
1 inch = 3 feet
(One inch represents an actual distance of 3
feet)
1:24
(1 unit represents an actual distance of 24
units)
Scale Factor
Example: Suppose a scale model has a scale of
2 inches = 16 inches. The scale factor is 2
or 1
16
8
The lengths and widths of objects of a scale
drawing or model are proportional to the
lengths and widths of the actual object.
Example 1: Find Actual
Measurements
A set of landscape plans shows a flower bed that is
6.5 inches wide. The scale on the plans is 1 inch
= 4 feet.
What is the width of the actual flower bed?
Let x represent the actual width of the flower bed.
Write and solve a proportion.
Plan width----> 1 inch = 6.5 inches<---plan width
Actual width--> 4 feet x feet <-----actual width
1x = 46.5 cross products
x= 26 The actual flower bed width is
26 feet.
From the last example, what is the scale
factor?
To find the scale factor, write the ratio of 1
inch to 4 feet in simplest form.
1inch = 1 inch
Convert 4 feet
4 feet 48 inches
to inches
The scale factor is 1 . That is , each
48
measurement on the plan is 1 the actual
measurement.
48
Example 2: Determine the Scale
In a scale model of a roller coaster, the highest
hill has a height of 6 inches. If the actual
height of the hill is 210 feet, what is the
scale of the model?
Model height---> 6 inches = 1 inch <--model height
Actual height--->210 feet x feet <--actual height
6x = 210
6x = 210
6
6
x= 35
So, the scale is 1” =
35 feet
Example 3: Construct a Scale
Drawing
A garden is 8 feet wide by 16 feet long. Make a scale drawing of
the garden that has a scale of 1 in. = 2ft.
4
Step 1: Find the measure of the garden’s length on the drawing.
Let x represent the length.
drawing length--> .25in = x in <--drawing length
actual length--> 2 ft
16ft <---actual length
.2516 =2x
4 = 2x
2=x
On the drawing, the length is 2 inches
• Step 2: Find the measure of the garden’s width on
the drawing. Let w represent the width.
drawing width--> .25 in = w inches <--drawing width
actual width ---> 2 feet
8 feet <---actual width
.258 = 2w
2 = 2w
1=w
On the drawing the width is 1 inch.
• Step 3: Make the scale drawing.
Use 1/4” grid paper. Since 2” = 8 squares and 1 inch =
4 squares, draw a rectangle that is 8 squares by 4
squares.
<------------------------ 16 ft--------------------->
8 ft
Your Turn!
On a set of architectural drawings for an office
building, the scale is 1/2” = 3 feet. Find the actual
length of each room.
.5” = 2”
Lobby: 2 inches
3ft x ft
.5x = 6
x = 12
Cafeteria: 8.25 inches
.5” = 8,25”
3ft
x ft
.5x = 24.75
x = 49.5
The actual length
of the lobby is 12 ft
The actual length of the
cafeteria is 49.5 feet
Your Turn, Again!
In an illustration of a honey bee, the length of the bee
is 4.8 cm. The actual size of the honeybee is 1.2
cm. What is the scale of the drawing?
4.8 cm = 1cm
1.2 cm x cm
4.8x = 1.2
x = .25
The scale of the drawing is 1 cm = .25cm
• Extra Practice sheets are by the door on
your way out, be sure to grab one!
• Quiz over 6-1 thru 6-3 Tomorrow!