MathGeometry & TrigonometryMedium frequency
SAT Math: Ratios in Similar Figures (Area & Volume)
23+ practice questions in Praczo
What you need to know
The concept, explained
- 1
If two similar figures have a side ratio of a:b (or a scale factor of k), their proportions scale up non-linearly.
- 2
The ratio of their perimeters is exactly the same as the side ratio (a:b).
- 3
The ratio of their AREAS is squared: a²:b² (or k²).
- 4
The ratio of their VOLUMES is cubed: a³:b³ (or k³).
- 5
If a triangle's sides are doubled, its area is quadrupled (2² = 4).
Common mistakes
- ✗ Assuming that if sides double, the area also doubles.
- ✗ Taking the square root of the volume ratio to find the side ratio instead of the cube root.
Try a sample question
SAT-style practice
Two similar cylinders have heights in the ratio of 2:3. What is the ratio of their volumes?
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