KS3 Maths

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Scale Drawings

KS3 Maths Ratio, Proportion and Rates of Change Scale Drawings

A scale drawing is a type of drawing that accurately represents an object but adjusts its size using a particular ratio, known as the scale factor.

Some common scale factors are 1:50, 1:100 and 1:500, which means that one unit on the drawing equals 50, 100 or 500 of the same units in real life.

Uses of Scale Drawings

There are many uses of scale drawings. Architects use scale drawings to design buildings, engineers employ them to map out machinery, and even cartographers (the people who make maps) rely on them.

In a scaled-down drawing, the relative sizes or proportions between the different features remain the same even though the overall size is smaller. This is a fundamental aspect of scale drawings. It’s essentially just a smaller version of the building.

However, scale drawings can also be a larger representation of very small objects, such as:

  • Electronic components (e.g. microchips)
  • Mechanical parts (e.g. gears and screws)
  • Jewellery

A typical scale drawing includes units (like cm or inches), a stated scale factor, and labels to identify different parts of the drawing. Knowing the scale factor and units is required for both creating and interpreting scale drawings.

How to Create a Scale Drawing

To create a scale drawing:

  • Step 1: Decide on the scale factor that you’ll use.
  • Step 2: Measure the actual dimensions of the object.
  • Step 3: Use the scale factor to calculate the dimensions on the drawing.
  • Step 4: Accurately draw the object using the scaled-down dimensions.

For example, let’s say you’re drawing a room with real-world dimensions of 5 \ m \times 6 \ m. You decide to use a 1 : 50 scale to create your drawing.

1. Determine the Scale Factor: In this case, the scale factor is 1 : 50. This means that 1 unit on the drawing represents 50 identical units in real life. The scale tells you that 1 cm on the drawing will represent 50 cm (or 0.5 m) in the actual room.

2. Measure the Real-World Dimensions: The actual room measures 5 \ m in width and 6 \ m in length.

3. Calculate the Scaled Dimensions: To find the dimensions for your drawing, you’d divide each of the real-world dimensions by the real-world unit represented by one drawing unit. In this case, one drawing unit (1 cm) represents 50 cm in real life. Therefore. 5 \ m = 500 \ cm and 6 \ m = 600 \ cm.

  • For the width: \frac{500 \ cm}{50} = 10 \ cm
  • For the length: \frac{600 \ cm}{50} = 12 \ cm

4. Create the Drawing: With the scaled dimensions calculated, you can now accurately draw the room on paper (or digitally) using the dimensions 10 \ cm \times 12 \ cm.

Reading a Scale Drawing

To read a scale drawing, you’ll need to reverse the process:

  • Step 1: Identify the scale factor.
  • Step 2: Measure the dimensions on the drawing.
  • Step 3: Use the scale factor to find the actual dimensions.

For example, suppose you have a scale drawing of a garden, and the scale mentioned on the drawing is 1:100. The drawing shows the garden to be 4 \ cm \times 3 \ cm.

1. Identify the Scale Factor: The first thing you notice is the scale factor mentioned on the drawing, which is 1 : 100. This means that 1 cm on the drawing represents 100 cm (or 1 m) in real life.

2. Measure the Dimensions on the Drawing: You measure the dimensions on the drawing and find that it is 4 \ cm wide and 3 \ cm long.

3. Find the Actual Dimensions: Now, to find the actual dimensions of the garden, you’ll multiply the drawing dimensions by the real-world unit represented by one drawing unit (1 cm). In this case, 1 cm on the drawing equals 1 m (or 100 cm) in real life.

  • For the width: 4 \ cm \times 100 = 400 \ cm (or 4 \ m)
  • For the length: 3 \ cm \times 100 = 300 \ cm (or 3 \ m)

So, by reversing the process, you can determine that the actual size of the garden is 4 \ m \times 3 \ m.

Practice Questions

Question 1:

If a room is drawn as 4 cm by 3 cm on a 1 : 100 scale, what are its real dimensions?

4 \ cm \times 100 = 400 \ cm and 3 \ cm \times 100 = 300 \ cm

Question 2:

A garden drawing measures 8 cm by 6cm and has a scale factor of 1 : 50. What are the real dimensions of the garden?

8 \ cm \times 50 = 400 \ cm and 6 \ cm \times 50 = 300 \ cm

Question 3:

A tower is shown to be 20 cm tall in a drawing with a scale factor of 1 : 200. How tall is the actual tower?

20 \ cm \times 200 = 4,000 \ cm or 40 \ m

Question 4:

You have a field drawn on a scale of 1 : 250 and the dimensions on the drawing are 15 cm by 10 cm. What’s the actual area of the field in square metres?

First, find the real dimensions: 15 \ cm \times 250 = 3,750 \ cm and 10 \ cm \times 250 = 2,500 \ cm

Then, find the area: 3,750 \ cm \times 2,500 \ cm = 9,375,000 \ cm^2, which is equal to 937.5 \ m^2

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