LCAT Math, Geometry and Trigonometry
Area and volume for the LCAT: lesson and practice
Know which formula matches the shape and use the radius, not the diameter. When all lengths are multiplied by k, area is multiplied by k² and volume by k³.
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No calculator on the LCAT. LUMS’s official guidelines say calculators are not allowed, so every practice question here can be solved by hand.
| 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
How does scaling affect area and volume?
Multiplying lengths by k multiplies area by k² and volume by k³.
Is area and volume tested on the LCAT?
Yes. It falls under Geometry and Trigonometry, one of the content domains LUMS lists for the LCAT in its official sample questions.
Can I practice this without a calculator?
Yes. Every practice question here can be solved by hand, because calculators are not allowed on the LCAT.