Areas of 2D figures and volumes of 3D solids, including composite shapes and problems where scaling changes area or volume.
65
Total questions
33
Easy
21
Medium
11
Hard
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.
Straight from the Grind1600 question bank — try each one before revealing the answer.
Correct answer: D
Choice D is correct. The area A of a rectangle is A = l × w. Substituting 15 for l and 8 for w yields A = 15 × 8 = 120. Choice A is incorrect (this is l + w). Choice B is incorrect (this is the perimeter 2(l + w)). Choice C is incorrect (may result from calculation errors).
Correct answer: 12
The volume of a cone is V = (1/3)πr²h. The height is 4 times the radius, so h = 4r. Substitute: V = (1/3)πr²(4r) = (4/3)πr³. Set (4/3)πr³ = 36π. Dividing both sides by π gives (4/3)r³ = 36, so r³ = 27 and r = 3. The height is h = 4r = 4(3) = 12. (Stopping at the radius gives 3; the question asks for the height.)
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.
65 Area & Volume questions with step-by-step explanations, woven into a day-by-day study plan built for your test date.
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