Smart Math guide · Geometry Smarts

Scale Factors Affect Area and Volume Differently

If lengths scale by k, areas scale by k² and volumes by k³.

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The method

How to use it

  1. Identify the linear scale factor k.
  2. Square k for area or cube k for volume.
  3. Apply to the original measure.
Worked example

See it in action

Doubling every dimension makes area 4× and volume 8×.

Check your thinking

How to verify it

A 2×2×2 cube has volume 8 compared with a 1×1×1 cube.

Keep learning

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