Three-Dimensional Figures — Quick Reference Cheatsheet
A focused companion to the main Three-Dimensional Figures topic page on SAT Math.
SAT Math Geometry & Trigonometry One-page reference
This is a one-page reference for Three-Dimensional Figures on the SAT math section. Compute volume and surface area for prisms, cylinders, pyramids, cones and spheres. Use it as a printable cheatsheet before test day, or as a refresher right before you attempt the worked questions on the main Three-Dimensional Figures topic page.
What this topic is
A Three-Dimensional Figures question tests your ability to apply geometric formulas, recognise special triangles, and use right-triangle trigonometry. Sketch the diagram before computing — every time.
Core formulas you must memorise
- Pythagorean: a² + b² = c²
- 30-60-90 sides: 1 : √3 : 2
- 45-45-90 sides: 1 : 1 : √2
- Circle: A = πr² ; C = 2πr
- SOH-CAH-TOA
- Pythagorean identity: sin²θ + cos²θ = 1
If any of these formulas are not yet automatic, drill them via the Geometry & Trigonometry formula sheet. Memorisation is fastest when you write each formula out by hand five times in a row, then quiz yourself the next morning.
How to spot this question type on the test
SAT questions on Three-Dimensional Figures typically present in one of three ways: as a pure symbolic problem ("solve for x"), wrapped in a word problem (a real-world scenario you must translate), or hidden inside a longer multi-step question where Three-Dimensional Figures is just the first or last step. Train yourself to recognise the signature — a particular word, equation form, or diagram — and you will halve your reading time.
The 30-second decision
The SAT reference sheet gives you area and volume formulas but NOT the trig identities or the equation of a circle. Memorise those.
If you have 60 seconds before the question
Glance at the answer choices first. If they are widely spaced, estimate; if they are close, you must be exact. Sketch any diagram involved. Identify which of the formulas above applies. Then attempt — and if you cannot finish in 90 seconds, mark and move on. There is no penalty for guessing on either the SAT or the ACT, so always bubble in.
Drill set
Re-attempt the six worked Three-Dimensional Figures questions with this cheatsheet open. Then close it and re-attempt them from memory. If you can solve all six without peeking, this topic is locked in.
Related study material
For broader test-prep tactics, see our Three-Dimensional Figures strategy guide. For category-wide context, browse all Geometry & Trigonometry topics. For score-targeted study plans, see the score-band guides.