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Scale Factor & Scale Drawings

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Scale Factor &

Scale Drawings

Understanding Scales

All scale drawings must have a scale written on them. Scales are usually expressed as ratios.

Normally for maps and buildings the ratio:

Drawing length: Actual length

For maps the ratio is normally in the ratio:

Map distance: Actual Distance

Example: 1cm : 100cm

The ratio 1cm:100cm means that for every 1cm on the scale drawing the length will be 100cm in real life

Example: 1:10000

The ratio 1:10000 means that the real distance is 10000 times the length of one unit on the map or drawing.

Scale Factor

How to find Scale Factor

- When a figure is dilated, its size is changed by multiplying the length of each side by a scalefactor. All angles remain the same and so the new shape (or image) is similar to the original.
- Can be found by dividing a new side length by the original side length.

- When going from a small shape to a larger shape the scale factor is greater than 1. (Enlargement)

- When going from a large shape to a smaller shape the scale factor is
- less than 1. (Reduction)

- Determine the corresponding side lengths.
- Determine if you are making a larger shape or a smaller shape.
- Determine if the scale factor is greater than or less than 1.
- Write the correct ratio.

new

SF

old

Scale Factor

Scale factor = new measurement

old measurement

Old measurement x SF = new measurement

- Scale factor more than 1 => shape gets bigger
- (Enlargement)
- Scale factor less than 1 => shape gets smaller
- (Reduction)
- Congruent shapes are similar shapes with SF = 1

Vocabulary

scale model

scale factor

scale

scale drawing

- The scale can be written as a scale factor, which is the ratio of the length or size of the drawing or model to the length of the corresponding side or part on the actual object.
- Scale Factor needs to be the SAME UNITS!

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

gauge model train is .

1

87

1

87

This means that each dimension of the model is of the corresponding dimension of the actual train.

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 drawingis a proportional drawing of an object. Both scale drawings and scale models can be smaller or larger than the objects they represent.

If you have ever seen Jurassic

Park, you saw how big the

dinosaurs were compared to the

people. Pretend that they made

a large Human to watch over the

animals. What would be the scale

factor if a 64 inch person was

made to be 160 feet?

The scale factor tells you

how many times bigger than

normal that person really is.

You must make all units of

measure the same.

64 inches

64 inches

64 inches

=

=

160 feet

1920 inches

160 x 12

Now take the:

64 inches

And simplify

1920 inches

1/30 inches

This means that the person

was created 30 times his

normal size.

The scale factor of the pool is

1 to 20 yards.

Or

=

Scale Factor

Keep like

units in the same fraction.

Inches = yards

Inches yards

Setting up Proportions

Remember

- There is more than one way to set up a proportion correctly!
- Cross Multiply!
- Use common sense!

Tom is drawing a blueprint for a rectangular shed he wants to build. The scale factor is 1 ft. to inch. If the dimensions of the blueprint are 1 in. by 2 inches, what are the actual dimensions of the shed going to be?

Write a Proportion

Using Scale Factor

inch to 1 foot

If the length in inches is 2 inch, what would the actual length be in feet ?

Write a ProportionUsing a Scale Factor

Scale Drawings

What are scale drawings?

Scale drawings are everywhere!

Scale Drawings

On Maps

Vehicle design

Footprints of houses

Can you think of any more?

6cm

Scale 1 cm = 1 m

Length of units = 6 m

Scale in everyday life: kitchen design

5

Scale in everyday life: maps

Scale 1 : 1 000 000

Scale in everyday life: plans

decking

path

pool

Scale 2 cm = 1 m

7

Using A Scale Drawing

When objects are too small or too large to be drawn or constructed at actualsize, people use a scale drawing or a model.The scale drawing of this tree is 1:500If the height of the tree on paper is 20 inches, what is the height of the tree in real life?

The scale is the relationship between the measurements of the drawing or model to the measurements of the object.

In real-life, the length of this van may measure 240 inches. However, the length of a copy or print paper that you could use to draw this van is a little bit less than 12 inches

Map Scales

- Map Scales (Legends) are used to find distances on a map.
- For example, if your map legend tells you that of an inch represents 50 miles, how could you find the mileage for a 2 inch distance on the map?

Map Scales

Ratios and proportions can be used to find distances using a scale.

Example:

1 inch = 15 miles

The distance from Jacksonville to Smithtown on a map is 4 inches. How many miles are between these cities?

1 in.

15 mi.

4 in

n

=

The distance between the two cities is 60 miles.

1n =

60

n = 60