G4 · Draw and describe simple exploded views and scaled components

Alberta Grade 11 Mathematics

Geometry

Showing how parts fit together and how drawing sizes represent real sizes

What you will learn

• Describe what an exploded view shows and how it helps with assembly.
• Draw or interpret a simple exploded view with clear labels and parts in a useful order.
• Use a scale to relate a component’s drawing measurement to its actual measurement.
• Check that labels, units, and component sizes make sense.

1. What an exploded view shows

• An exploded view separates components to make them easier to see.
• The positions of the parts should still show how they fit together.
• Use clear labels and state the number of repeated parts.

2. Scales and component measurements

• Scale compares a drawing size with a real size.
• At CAD 1:n, multiply a drawing measurement by $n$ to find the real measurement.
• Use the same unit on both sides of a scale comparison.

3. Making a useful drawing

• Arrange exploded parts to make their connections easy to understand.
• State the scale and units when the drawing gives measurements.
• Mark a sketch as not to scale if its proportions are only approximate.

4. Check the result

• Check whether the real size is larger or smaller as the scale requires.
• Keep units visible and convert only when needed.
• A good description names parts and explains their arrangement.

Worked example

Exploding a small workbench into parts

1. Identify the components
   The main component is the workbench top. The other components are four matching legs and one lower shelf. Naming the quantity of legs prevents a reader from thinking that only one leg is included.
2. Place parts near their connections
   Show the top as the central piece. Place one leg just below each corner where it attaches. Put the shelf below the top and between the legs, near the height where it will be fixed. Leave small gaps so the separate parts can be seen.
3. Add labels and dimensions
   Label the top, the four legs, and the lower shelf. State the top dimensions as length, width, and thickness. The dimensions describe the top, not the gaps in the exploded view.
   $$120\text{ cm}\times60\text{ cm}\times4\text{ cm}$$

Worked example

Finding a real component size from a drawing

1. Interpret the scale
   The scale 1:8 means each centimetre on the drawing represents 8 centimetres on the real strip. Both measurements can be compared directly because they use centimetres.
   $$1\text{ cm on drawing}=8\text{ cm real}$$
2. Calculate the real length
   Multiply the drawing length by 8. This accounts for the fact that the real strip is eight times as long as its drawing.
   $$3.5\times8=28\text{ cm}$$
3. Check the result
   The real strip should be longer than its drawing because this is a reduced drawing. A length of 28 cm is eight times 3.5 cm, so it matches the scale.

Worked example

Choosing dimensions for a scaled panel

1. Read the scale direction
   At 1:4, one drawing unit represents four real units. To find drawing measurements from the real measurements, divide each real measurement by 4.
   $$\text{drawing measurement}=\text{real measurement}\div4$$
2. Calculate both drawing dimensions
   Divide the height and width separately. Keeping each dimension paired with its own label avoids confusing the panel’s height with its width.
   $$80\div4=20\text{ cm},\quad30\div4=7.5\text{ cm}$$
3. Label the drawing
   Draw a rectangular panel and label its height as 20 cm and its width as 7.5 cm. State the scale as 1:4. In a larger exploded view, place the panel near the other storage-unit parts where it belongs.

Common mistakes and how to avoid them

Lesson summary

• An exploded view separates components while keeping their positions useful for understanding assembly.
• Clear labels, quantities, and sensible part placement make an exploded view easier to use.
• A scale compares drawing measurements with real measurements.
• At 1:n, multiply a drawing measurement by n to find the real measurement; divide a real measurement by n to find the drawing measurement.
• Use matching units, state the scale, and check that the result is reasonable.

Check your understanding

Key terms

Component

One part of a larger object.

Exploded view

A drawing that separates an object's parts slightly to show how they fit together.

Scale

A comparison between a drawing measurement and the matching real measurement.

Assembly order

The sequence in which parts are put together.

Continue through Math 20-3

View the complete Math 20-3 Alberta Grade 11 Mathematics curriculum and lessons

• G3 · Model 3-D objects and draw their top, front, and side views
• N1 · Use and verify strategies for numerical puzzles and games
• G1 · Solve problems involving two or three right triangles
• G2 · Solve practical scale and scale-diagram problems
• M2 · Solve volume and capacity problems with SI and imperial units
• N3 · Explain and calculate compound-interest growth

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About this lesson and its review

Published by DoAssignment. This reviewed lesson follows Alberta Grade 11 Mathematics (Math 20-3), expectation G4. It is a study resource, not an official curriculum publication.

Before publication, content is checked for structure, mathematical or chemical notation, calculations, course boundaries, and readability. Errors can still occur, so corrections are welcomed.

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