SAT Area and Volume Questions
Area, surface area and volume of standard and combined shapes.
In short
- Area and Volume is part of Geometry and Trigonometry, about 15% of the scored Math questions: 5 to 7 on every test.
- Math questions from all four areas are mixed in each module and arranged from easiest to hardest.
- Cylinder volume formula is the trap Rivie's practice tests set most often in Area and Volume questions.
Common traps
Most common first, from Rivie's ten practice tests.
Cylinder volume formula
Cylinder volume = πr²h. The wrong choice mixes up surface area (2πrh + 2πr²), uses diameter for r without halving, or applies the cone formula (1/3 πr²h).
The usual mistake: You substitute diameter where the formula expects radius, or grab the surface-area formula because both involve πr. The fix is to write the formula explicitly before plugging in.
Sphere volume formula
Sphere volume = (4/3) π r³. The wrong choice drops the 4/3, uses surface area (4πr²), or substitutes diameter for r without halving.
The usual mistake: You forget the 4/3 coefficient (the most-frequently-mismemorized part of the formula). Or you use diameter instead of radius and your answer is 8× too big.
Try a question
From Rivie's practice tests. Pick an answer to see why it is right or wrong.
A right circular cylinder has radius 4 and height 10. What is the volume of the cylinder?
Video lessons
Free on YouTube, picked for this topic.