Lesson 17 — Activity 1: Scale Drawings


Getting Ready



In this activity, you will learn about scale drawings.


It is very important to have a plan whenever you build anything. This gives you something to refer back to if you are not sure what to do, and also you can see what the finished product will look like.


However, most things that people build are too large to have a plan that is the same size as what is being built. Can you imagine trying to build a house with a paper plan that was 40 feet wide by 46 feet long? It would be impossible to use! Because of this, people use scale drawings.


 

Courtesy of Pixabay

Think about This:


A scale model is a 3-D replica of an object.


Scale models are used in many workplace situations, such as:

  • models of car engines are helpful to automotive mechanics when talking to customers about problems
  • models of human hearts are useful when used in the training of healthcare workers
  • models of shopping malls are developed to help planners makes road and traffic flow decisions


Courtesy of Getty


A Scale Drawing

A scale drawing is a drawing in which the lengths are a reduction or an enlargement of the actual lengths of an object. This can be very detailed, like a house plan, or it can be very simple, like a general drawing of a shape.

Another word for a scale drawing that is being used to build something is a blueprint. If you have ever looked at floor plans for a house or an electrical wiring plan, you have looked at both a scale drawing and a blueprint.

Whenever you are given a scale drawing to look at, you will also be given a scale factor. A scale factor is the ratio of the new size to the corresponding old size. For example, if the scale factor was 1:10 cm on a model car, this would mean that each centimetre on the model would correspond to 10 centimetres on the actual car.

  
Courtesy of Getty

Here's another example:




Courtesy of Pixabay

The drawing above also has a scale of "1:10," so anything drawn with the size of "1" would have a size of "10" in the real world, so a measurement of 150 mm on the drawing would be 1,500 mm on the real horse.

About Reductions and Enlargements

Reductions

A map is a reduction of an actual place or location. Scales show reduction when the first number in the scale is smaller than the second number.

 Example: 1:20 (20 times smaller)

 1:2,000 (2,000 times smaller)


Courtesy of Getty

Enlargements

Scales show enlargement when the first number in
the scale is larger than the second number.

Example: 10:1 (10 times larger)

250:1 (250 times larger)


Determining Scale Using Ratios

You may be given information on a scale drawing and asked to calculate the actual length of an object.

For example, a hallway is measured to be 3.5 cm long on a blueprint. The scale factor of the drawing is 1:100. What is the length of the actual hallway?

Courtesy of Pixabay
In order to solve this, we can set up a ratio. First, enter the scale as a fraction. Second, put the information you have been given on the same level as the same information in the first fraction.

You would enter the scale as:


Because the information you have been given deals with the scale size, you will enter that information on the same level and use an "x" to represent the unknown information.




Once you have set up the ratio, you can cross multiply to solve for "x."


3.5 x 100 = x
350 = x

The actual hallway is 350 cm long.


Try This:

Courtesy of Getty

The length of the new gym in a school is measured to be 2.2 cm long on a blueprint. The scale factor of the drawing is 1:1,000. What is the length of the new gym?

 

       1         =    2.2
    1,000           x

2.2 x 1,000 = x

2,200 = x

The gym is 2,200 cm long.





But what if we were asked to go the other way? Let's say you are given a length of 257 m and need to draw a picture of it but can only use a scale of 1 cm = 10 m. How long would you draw the line?

We can use the same steps to solve this as above, except you will change where the "x" is.





The line you would need to draw would be 25.7 cm long.

Please note that if there are no units in the scale, the units will be the same as those found in the actual measurement.




  Self-check!

Try This!

Try this activity to practice working with scales.


You are given a map with a scale of 1 cm : 1000 m. On the map you measure from Point A to Point B and find that it is 5.42 cm long. What is the real distance between Point A and B?

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The real distance between Point A and Point B is 5420 metres.


You are given a rectangle with a length of 5 m and a width of 3 m. Your teacher asks you to draw a scale drawing in which 1 cm : 1 m. How long and how wide would your scale drawing be?

Step 1: Find the length.

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The length of the scale drawing rectangle would be 5 centimetres.


Step 2: Find the width.

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The width of the scale drawing rectangle would be 3 centimetres.


A model of the USS Nimitz (an aircraft carrier) is 20 cm long. On the box it has a scale of 1 cm : 50 ft. How long is the actual aircraft carrier?

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The actual aircraft is 1000 ft long.