Area measures a two-dimensional region, surface area measures exposed faces, and volume measures three-dimensional capacity. SAT problems often combine these formulas with unit conversion, similarity, or a missing dimension.
Essential concepts
\[A_{ riangle}= rac12 bh qquad A_{ ext{circle}}=pi r^2 qquad V_{ ext{cylinder}}=pi r^2h\]
For prisms and cylinders, volume equals base area times perpendicular height.
SAT strategy and application
Find cylinder volume
A cylinder has radius \(3\) and height \(5\). Find its volume.
- Find the base area
\(pi r^2=pi(3)^2=9pi\).
- Multiply by height
\(9pi(5)=45pi\).
Volume: \(45pi\) cubic units.
Mistakes and traps
Check your understanding
Every side length of a rectangle is tripled. By what factor does its area change?
- 3
- 6
- 9
- 27
Show answer and explanation
Answer: \(9\)
Area scales by the square of the length factor: \(3^2=9\).
Key takeaways
What to remember
- Match the formula to the requested type of measurement.
- Convert units before calculating and label squared or cubed units.
- Use decomposition or subtraction for composite figures.
- Apply squared and cubed scale factors to area and volume.
Continue learning
Put these notes into practice
Apply the ideas with SAT-style questions, then reinforce key details with flashcards.