Problems in three dimensions (AQA GCSE Further Maths): Flashcards

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Problems in three dimensions
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What are the 3 dimensions in 3D geometry?

Length, width, height

Effective approach for 3D problems

Break into smaller 2D calculations

Great circle route

Shortest path on Earth's surface (curved on flat maps)

Isometric projection purpose

Represent 3D objects accurately on paper

Isometric: east-west lines

Draw as horizontal lines

Isometric: vertical lines

Draw as vertical lines

Isometric: north-south lines

Draw sloping at about 30°30° to horizontal

Isometric: hidden edges

Use dotted lines

True shape diagram function

Shows right angles as genuine 90°90° (not distorted)

Why true shape diagrams needed

Right angles appear distorted in 3D views

Creating true shape diagram: first step

Identify face with right angle, draw separately as 2D

Common error in 3D calculations

Using distorted angles from 3D views

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