Drawing Scaled Plans Revision Notes for Grade 11 NSC Matric Mathematical Literacy

Drawing Scaled Plans

What is drawing scaled plans?

Drawing scaled plans is the process of creating accurate technical drawings where real-world dimensions are proportionally reduced to fit on paper. This is different from reading existing plans - instead, you start with actual measurements and use a given scale to determine how large to draw objects on your plan.

When architects and draftsmen design buildings, they use this process to create floor plans, elevation plans, and design drawings. They know the actual sizes of rooms, doors, windows, and furniture, and they need to draw these items at the correct scaled size.

Understanding the relationship

The key relationship for drawing scaled plans is straightforward. When you want to draw something on a plan, you need to:

Know the actual dimension (real-world size)
Apply the given scale
Calculate the plan measurement (how big to draw it)

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This fundamental relationship shows how actual dimensions are converted to plan measurements through scaling. Understanding this connection is essential for creating accurate technical drawings.

The calculation process

To find the plan measurement, follow this formula:

$\text{Plan measurement} = \frac{\text{Actual dimension}}{\text{Scale ratio}}$

Understanding scale ratios

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A scale like 1:75 means:

1 unit on the plan represents 75 units in real life
The plan drawing is 75 times smaller than the actual object
To find the plan size, divide the actual size by 75

Worked example

Let's work through a complete example step by step.

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Worked Example: Drawing a Door at Scale

Problem: A door has an actual height of 2,1 m. You need to draw this door on a plan using a scale of 1:75. What should be the height of the door on your drawing?

Step 1: Identify the given information

Actual door height = 2,1 m
Scale = 1:75

Step 2: Understand what the scale means

Scale 1:75 means the actual door height is 75 times larger than the plan measurement
Or the plan measurement must be 75 times smaller than the actual height

Step 3: Apply the formula

$\text{Plan measurement} = \frac{\text{Actual dimension}}{\text{Scale ratio}}$
$\text{Plan measurement} = \frac{2,1 \text{ m}}{75} = 0,028 \text{ m}$

Step 4: Convert to appropriate units

$0,028 \text{ m} = 2,8 \text{ cm} = 28 \text{ mm}$

Answer: The door should be drawn 2,8 cm (or 28 mm) tall on the plan.

Additional worked examples

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Worked Example: Classroom Length

A classroom is 8 m long. Draw this at a scale of 1:100.

Solution:

Actual length = 8 m
Scale = 1:100
Plan measurement = $\frac{8 \text{ m}}{100} = 0,08 \text{ m} = 8 \text{ cm}$

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Worked Example: Window Width

A window is 1,5 m wide. The scale is 1:50.

Solution:

Actual width = 1,5 m
Scale = 1:50
Plan measurement = $\frac{1,5 \text{ m}}{50} = 0,03 \text{ m} = 3 \text{ cm}$

Exam tips and common mistakes

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Key Points to Remember:

Always divide the actual dimension by the scale ratio
Check your units carefully - convert to cm or mm for drawing measurements
The scale ratio is the second number (in 1:75, the ratio is 75)
Larger scale ratios make smaller drawings (1:100 is smaller than 1:50)

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Common Exam Traps:

Mistake: Multiplying instead of dividing
Mistake: Using the wrong number from the scale (using 1 instead of 75)
Mistake: Forgetting to convert units appropriately
Mistake: Confusing this process with reading existing plans

Remember!

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Essential Takeaways:

Drawing scaled plans means starting with actual dimensions and calculating plan measurements
Use the formula: $\text{Plan measurement} = \frac{\text{Actual dimension}}{\text{Scale ratio}}$
Scale 1:75 means the plan is 75 times smaller than real life
Always divide the actual dimension by the scale ratio
Convert your final answer to centimetres or millimetres for practical drawing measurements

Drawing Scaled Plans (Grade 11 NSC Matric Mathematical Literacy): Revision Notes