SAT Math · Geometry and Trigonometry

Area & Volume on the Digital SATWhat it tests, how to approach it, and where students get trapped

Areas of 2D figures and volumes of 3D solids, including composite shapes and problems where scaling changes area or volume.

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Area & Volume in Our Question Bank

Total questions

Easy

Medium

Hard

These counts cover the full Grind1600 bank. On the Free plan you get the first 5 easy, 5 medium, and 5 hard questions in Geometry and Trigonometry.

What the SAT Actually Tests

Area and volume questions range from direct formula application (the formulas are given in the test's reference sheet) to composite figures, shaded regions, and scaling problems — if a cylinder's radius doubles, what happens to its volume? Real-world versions involve paint coverage, packing boxes, and material costs.

Use the reference sheet — it's there for a reason and lists every needed formula. For composite shapes, decompose into pieces or subtract the hole from the whole. For scaling, remember the exponent rule: lengths scale by k, areas by k², volumes by k³. A doubled radius quadruples a circle's area and (in a cylinder) quadruples volume through the r² term.

Original Area & Volume Practice Questions

These fixed public samples come from Grind1600's original question bank. Choose an answer and check your reasoning before reading the explanation.

Question 1easy

What is the area, in square centimeters, of a rectangle with a length of 15 centimeters and a width of 8 centimeters?

A)23B)46C)60D)120

Question 2medium

Triangle P is similar to triangle Q. A side of triangle P has length 10 centimeters and corresponds to a side of triangle Q that has length 15 centimeters. If the area of triangle P is 40 square centimeters, how many more square centimeters is the area of triangle Q than the area of triangle P?

A)20B)50C)90D)130

Traps to Avoid

Using the diameter as the radius in circle and cylinder formulas.
Scaling area or volume linearly when a dimension changes — missing the k² / k³ effect.
Answering with the full figure's area when the question asks for the shaded region only.

Want more official questions for this skill?

The College Board Student Question Bank can filter official SAT questions by section, domain, skill, and difficulty. Read our question-bank workflow guide before choosing a set.

More Geometry and Trigonometry Skills

Lines, Angles & Triangles

Parallel-line angle relationships, triangle angle sums, similarity and congruence, and the triangle inequality.

Right Triangles & Trigonometry

The Pythagorean theorem, special right triangles, and SOH-CAH-TOA trigonometric ratios, including the sine-cosine complement relationship.

Circles

Circle equations in the xy-plane, arc length, sector area, central angles, and completing the square to find center and radius.

Continue With Geometry and Trigonometry Practice

Practice is sorted by domain and difficulty. On the Free plan you get the first 5 questions of each difficulty in Geometry and Trigonometry. Pro opens every question in the bank.

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Last reviewed August 29, 2026 · Grind1600 Editorial Team