IGCSE Maths Similar Shapes & Scale Factors Notes
Similar shapes have the same angles and proportional sides. Length, area and volume each scale by a different power of the scale factor.
Key concepts
- Similarity
- Same shape, corresponding angles equal and sides in the same ratio.
- Scale factor
- The ratio linking corresponding lengths of two similar shapes.
- Area & volume factors
- Area scales by k², volume by k³, where k is the length scale factor.
Key formulas
Area scale factor
k²
Volume scale factor
k³
Worked example
Two similar solids have length scale factor 2. The smaller has volume 15 cm³. Find the larger volume.
- 1Volume scale factor is k³ = 2³ = 8.
- 2Multiply: 15 × 8.
- 3State the larger volume.
Answer: 120 cm³
Common mistakes
✗ Using the length factor for area or volume.
✓ Square it for area (k²), cube it for volume (k³).
✗ Matching non-corresponding sides.
✓ Pair sides opposite equal angles.
✗ Inverting the scale factor.
✓ Divide larger by smaller (or vice versa) consistently.
Quick check
Try these, then reveal the answers.
Length scale factor 3 — area factor?Reveal answer
9
Length scale factor 2 — volume factor?Reveal answer
8
Are all circles similar?Reveal answer
Yes
Exam tips
- Identify corresponding sides before finding the scale factor.
- Remember k, k², k³ for length, area and volume.
- Check whether you are scaling up or down.
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Frequently asked questions
How does area scale for similar shapes?+
Area scales by the square of the length scale factor, so a length factor of 3 gives an area factor of 9.
What makes two shapes similar?+
Their corresponding angles are equal and their corresponding sides are in the same ratio.
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