SAT Math · Additional Topics in Math
Volume and surface area
Prisms, cylinders, cones, spheres, and pyramids.
What's tested in this subtopic
Items test the volume formulas for the standard solids and (occasionally) surface area. The SAT provides a reference sheet with most of these formulas; the question is whether you can read it under time pressure.
Tactics that actually move your score
Even though formulas are provided, memorize the common ones to save time. Sphere volume is 4/3 πr³ — the 4/3 is the most-forgotten coefficient. Cone is one-third of cylinder; pyramid is one-third of prism. The single biggest leverage point on most subtopics isn't learning more math — it's recognizing the test's preferred surface forms quickly enough that you don't burn 30 seconds re-reading the question. The first time you see a particular phrasing it might take you a full minute. The tenth time you see it, you should be reaching for your method before you've finished the sentence. Repetition is what builds that recognition. Fifteen problems in a row of the same shape is more useful than fifty mixed.
Practice questions (14)
- Easy A cylinder has radius 4 and height 8. What is its volume, in terms of π?
- Easy A cylinder has radius 7 and height 5. What is its volume, in terms of π?
- Medium A cylinder has radius 2 and height 12. What is its volume, in terms of π?
- Medium A cylinder has radius 3 and height 6. What is its volume, in terms of π?
- Medium A cylinder has radius 3 and height 12. What is its volume, in terms of π?
- Hard A cylinder has radius 8 and height 11. What is its volume, in terms of π?
- Easy A cylinder has radius 7 and height 3. What is its volume, in terms of π?
- Easy A cylinder has radius 2 and height 9. What is its volume, in terms of π?
- Medium A cylinder has radius 2 and height 6. What is its volume, in terms of π?
- Medium A cylinder has radius 3 and height 9. What is its volume, in terms of π?
- Medium A cylinder has radius 2 and height 11. What is its volume, in terms of π?
- Hard A cylinder has radius 6 and height 9. What is its volume, in terms of π?
- Easy A cylinder has radius 7 and height 8. What is its volume, in terms of π?
- Easy A cylinder has radius 5 and height 5. What is its volume, in terms of π?
How to drill
Work through the questions above untimed. After each one, read the worked solution from start to finish — even when you got it right. Note which solution method you used, and which method we used; if they differ, ask yourself which would have been faster on test day. Speed in SAT math comes from shortening your method-selection step, not from doing arithmetic faster. Most fast students are doing the same arithmetic everyone else is — they're just spending less time deciding what to do.
Once you can clear the easy and medium items in this subtopic at 90% accuracy, attempt a timed mini-set of ten hard items at 75 seconds each. If you finish in time and score 7+ correct, you've effectively mastered the subtopic for test purposes and can move on.