Scale and Scale Factor

Scale and Scale Factor

Growing and shrinking

Key Words

Scale Drawing: a proportional, two-dimensional drawing of an object

Scale Model: a proportional, three dimensional model of an object

Scale: a ratio that compares the measurement of the drawing or
model with actual measurements

Scale Factors: a scale factor where the units of measurement are the
same

Multiple Choice

What is a scale drawing?

• A two-dimensional representation of an actual object or place.

• This line segment from the center of a circle to a point on the circle.

• When two lines cross, they form two pairs of vertical angles across from one another.

• An image that has been made bigger and all the angles change size.

Find the actual distance

The distance between Cadillac and Detroit Michigan is 3.5 centimeters on the
map. If the scale is 1 cm = 50 mi, what is the distance between the two cities?

Step 1

set up a proportion

Step 2

solve the proportion

​Use the given scale as your first ratio

Find the scale size

The liquid outer core of Earth is 2300 Kilometers thick. A scale model of the
layers of Earth has a scale of 1 in : 500 km. How thick is the liquid outer core of
the model?

Step 1

set up the proportion

Step 2

Solve the proportion

​Use the given scale as your first ratio

Using a picture

How tall will the model be if the
scale is used?

Step 1 : Identify the scale

Step 2: set up the proportion

Step 3: Solve

Multiple Choice

This scale drawing shows a parking lot. What is the length of the longer side of the actual lot? 

• 63 m
• 235 m
• 315 m
• 630 m

Multiple Choice

A scale drawing of a house shows 9cm ×10cm. If 6cm=12 ft, what are the actual dimensions?

• 9ft x 10ft
• 1ft x 2ft
• 12ft x 6ft
• 18ft x 20ft

Scale Factor

BOTH parts of the ratio will be in the same unit

Usually written without units (usually the smaller of the units)

The scale for the model car is 1 : 14

This means that for every 1 unit (usually inches) on the model there is

14 units on the actual car

Find the scale factor

What is the scale factor
of this situation

-these are the same
unit so just set up a
ratio and convert one
of the numbers to one.

- set up as

Multiple Choice

What is the scale factor from the small fry to the large fry?

• 1/3

• 48

• 4

• 3

Multiple Choice

What is the scale factor from ΔDEF to ΔABC?

• 1/2
• 7/3
• 2
• 10/3

Multiple Choice

What is the scale factor from MNOP to ABCD?

• 2/3
• 1/2
• 3/2
• 2

Multiple Choice

What is the scale factor from Δ DEF to Δ ABC

• 2
• 3/2
• 2/3
• 1/2

Find the scale factor

The scale model of the monument is 10 inches tall. The actual measurement is
100 feet. What is the scale factor?

Step 1:

Find the scale of the model

Step 2: convert the units to ONE unit (usually the smaller one)

Find the scale factor

What is the scale factor of the
situation to the right?

Step 1: identify the scale

Step 2: convert the units into one
unit (usually into the smaller one)

Multiple Choice

A map of the property is being made with a scale of 2 centimeters is 3 meters. What is the scale factor?

• $$\frac{1}{150}$$

• $$\frac{2}{3}$$

• $$\frac{150}{1}$$

• $$\frac{3}{2}$$

Math Response

The longest aircraft carrier in the world, supercarrier USS Gerald R Ford, is 1,082 feet long. If you were to make a model using a scale of 1 inch equals 20 feet. What is the scale factor?

Type answer here

Correct Answer: \frac{1}{240}

Deg^°

Rad

Grow or shrink?

A scale factor that is less than 1 (one) shows that the “new” version is going to be
smaller than the original.

1 : 15 1/13

A scale factor that is greater than 1 (one) shows that the “new” version is going to
be larger than the original.

2 : 1 5/1

Multiple Choice

If the scale factor is greater than one, the new figure will be

• a reduction
• an enlargement
• a scale
• not proportional

Multiple Choice

sf = 0.8

• Reduction
• Enlargement

Multiple Choice

sf = 6/5

• Reduction
• Enlargement

Multiple Choice

Find side length X.

• 16
• 18
• 2.4
• 15