Scale drawings-and-scale-models-ppt

1. Scale Drawings and Scale Models
Learn to understand ratios and
proportions in scale drawings. Learn to
use ratios and proportions with scale.

2. Scale Drawings and Scale Models
Vocabulary
scale drawing
scale factor
scale model
scale

3. 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.
1
87
1
87

4. 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.

5. Scale Drawings and Scale Models
Identify the scale factor.
Additional Example 1: Finding a Scale Factor
13.5108Width (in.)
18144Length (in.)
BlueprintRoom
blueprint length
room length
= 1
8
1
8
The scale factor is .
Write a ratio using one of the
dimensions.
Simplify.
18
144
=
A scale factor is always the ratio of
the model’s dimensions to the actual
object’s dimensions.
Caution!

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
= 2
12
= 1
6
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 .
1
6
1
4
1
6
1
4

7. 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
5
1
Think:
poster
photo
= 5
1
36
l
= 5
1
5l = 36
l = 7.2
Write a proportion to find the
length l.
Find the cross products.
Divide.

8. 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
5
1
Think:
poster
photo
= 5
1
20.5
w
= 5
1
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.

9. 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.
1.5
60
= 7.5(in)
D (mi)
1.5 · d = 60 · 7.5
1.5d = 450
1.5d
1.5
= 450
1.5
d = 300
The distance between the cities is 300 miles.
Write a proportion.
Find the cross products.
Multiply.
Divide both sides by 1.5.