Scale Factor & Scale Drawings
Mar 31, 2015
Scale Factor &Scale Drawings
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.
Understanding Scales
Scale Factor
When a figure is dilated, its size is changed by multiplying the length of each side by a scale factor. 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)
1. Determine the corresponding side lengths.2. Determine if you are making a larger shape or a smaller shape.3. Determine if the scale factor is greater than or less than 1.4. Write the correct ratio.
How to find Scale Factor
𝐵𝑖𝑔𝐿𝑖𝑡𝑡𝑙𝑒
𝐿𝑖𝑡𝑡𝑙𝑒𝐵𝑖𝑔
Scale factor = new measurement old 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
Old measurement x SF = new measurementSF
new
old
Scale Factor
scale modelscale factorscalescale drawing
Vocabulary
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
This means that each dimension of the model is of the corresponding dimension of the actual train.
187
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 drawing is 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
160 feet64 inches
160 x 12
64 inches1920 inches
= =
Now take the:
64 inches
1920 inches And simplify
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
There is more than one way to set up a proportion correctly!
Cross Multiply!Use common
sense!
Remember…
Tom is drawing a blueprint for a rectangular shed he wants to build. The scale factor is 1 ft. to ¼ inch. If the dimensions of the blueprint are 1 ¼ in. by 2 inches, what are the actual dimensions of the shed going to be?
Write a Proportion Using Scale Factor
¾ inch to 1 foot
If the length in inches is 2 ¼ inch, what would the actual length be in feet ?
Write a Proportion Using a Scale Factor
Scale Drawings
Scale Drawings
On Maps
Footprints of houses
Vehicle design
What are scale drawings?Scale drawings are everywhere!
Can you think of any more?
Scale 1 cm = 1 m
6cm
Length of units = 6 m5
Scale in everyday life: kitchen design
Scale 1 : 1 000 000
Scale in everyday life: maps
Scale 2 cm = 1 m
pool path
decking
7
Scale in everyday life: plans
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 (Legends) are used to find distances on a map.
For example, if your map legend tells you that ½ 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 milesThe 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
1n =
60
n = 60
The distance between the
two cities is 60 miles.
Map Scales