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12 multiple-choice questions and 1 flashcards on Surface Area and Volume, about 8% of the High School Geometry bank. Every one carries a written rationale.
Surface Area and Volume is one of 13 chapters in CoStudy's High School Geometry bank, and it holds 12 of the bank's 150 multiple-choice questions — roughly 8% of the total. That proportion is not arbitrary: chapters follow the certifying body's published exam outline, and the number of questions in each is set by that domain's published weight, so the share of your practice time this chapter takes matches the share of the real exam it accounts for.
Studying by chapter is worth doing once you have a diagnostic score. A single overall percentage tells you whether you are close; it does not tell you which domain is dragging. Working a weak chapter in isolation, and re-testing it in isolation, is the fastest way to move a score that has stalled — and it is why the mock exams in CoStudy report by domain rather than as one number.
3 questions drawn from this chapter, with the full rationale shown — the controlling principle behind the right answer, and why each wrong option tempts and fails.
What is the volume of a cylinder with radius 4 and height 10?
Answer: E — 160π (V = πr²h = π · 16 · 10)
Cylinder volume: V = πr²h (area of circular base × height). π(4²)(10) = 160π. For cone: V = (1/3)πr²h. For sphere: V = (4/3)πr³. Memorize these standard volume formulas.
30-60-90 triangle: if shortest leg is 5, the hypotenuse is:
Answer: D — 10 (sides in ratio 1 : √3 : 2; hypotenuse = 2× shortest leg)
30-60-90 ratios: short:long:hyp = 1:√3:2. Short=5: long=5√3, hyp=10. 45-45-90: 1:1:√2. Memorize these special right triangles — common on geometry exams.
A cylinder has radius 5 and height 10. Its total surface area is:
Answer: B — 150π
A) Lateral surface only: 2πrh = 100π. B) Total SA = 2πrh + 2πr² = 2π(5)(10) + 2π(25) = 100π + 50π = 150π. C) Just the two bases. D) Half of the answer.
1 cards from the 1 in this chapter.
Volume of a cylinder with radius 5 and height 10. Use π ≈ 3.14.
≈ 785 cubic units.
These are a sample. The full Surface Area and Volume chapter runs 13 items with per-chapter progress tracking, on the web and in the iOS app.
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