Math, Geometry and Trigonometry, Stage 3
Area and volume on the SAT: lesson and practice
Know which formula matches the shape and use the radius, not the diameter. The SAT reference sheet lists every formula you need. When all lengths are multiplied by k, area is multiplied by k² and volume by k³.
Loading practice…
| Shape | Formula |
|---|---|
| Triangle | ½bh |
| Circle | Area πr², circumference 2πr |
| Box | lwh |
| Cylinder | πr²h |
| Cone | ⅓πr²h |
| Sphere | ⁴⁄₃πr³ |
For a shaded region, subtract: outer shape minus inner shape.
Common mistakes
Forgetting ½ for trianglesArea = ½ × base × height.
Diameter instead of radiusDiameter 10 means radius 5.
Linear scaling of areaDouble the sides: area × 4, volume × 8.
Sample questions with answers
1. A circle has radius 5. Its area?
- 10π
- 25π (correct)
- 100π
- 5π
πr² = 25π.
2. Every side of a square is tripled. Area multiplies by…
- 3
- 6
- 9 (correct)
- 27
3² = 9.
3. A cylinder has radius 6 and height 11. Its volume?
- 66π
- 132π
- 396π (correct)
- 1,584π
π(6²)(11) = 396π.
Frequently asked questions
Does the SAT give area and volume formulas?
Yes. Geometry and Trigonometry makes up about 15% of SAT Math, roughly 5 to 7 questions. A reference sheet with key formulas is available during the test.
How does scaling affect area and volume?
Multiplying lengths by k multiplies area by k² and volume by k³.
Should I leave answers in terms of π?
If the choices use π, yes. Otherwise, use the calculator.