Areas of 2D figures and volumes of 3D solids, including composite shapes and problems where scaling changes area or volume.
66
Total questions
33
Easy
24
Medium
9
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.
66 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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