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37 multiple-choice questions and 17 flashcards on Area, Surface Area, and Volume in Real-World Problems, about 25% of the 7th Math: Geometry bank. Every one carries a written rationale.
Area, Surface Area, and Volume in Real-World Problems is one of 6 chapters in CoStudy's 7th Math: Geometry bank, and it holds 37 of the bank's 150 multiple-choice questions — roughly 25% 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.
10 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.
The base of a triangular prism has area 15 cm². The prism length is 9 cm. Volume:
Answer: C — 135 cm³
C) V = base area · length = 15 · 9 = 135 cm³. A) Added. B) Halved (already used ½ in the base area). D) Doubled.
A regular hexagon has all sides equal to 5 cm. Its perimeter is:
Answer: B — 30 cm
Perimeter = 6 × 5 = 30 cm. (A) P = 5 × 5; (C) P = 12 × 5; (D) P = 3 × 5.
Volume of a triangular prism with triangular base area 12 and length 8:
Answer: C — 96
C) V = base area · length = 12·8 = 96. A) Added. B) ½·12·8 — but base is already computed. D) Off-by-one.
Using a scale of 1:100, a room measures 4 cm × 5 cm on a floor plan. Actual area?
Answer: D — 20 m²
Actual length: 4 × 100 = 400 cm = 4 m; width: 5 × 100 = 500 cm = 5 m; area = 4 × 5 = 20 m². (A) forgot scale; (B/C) converted units incorrectly.
A rectangular prism has volume 120 cm³, length 6 cm, and width 4 cm. What is its height?
Answer: A — 5 cm
V = lwh → 120 = 6 × 4 × h = 24h → h = 5. (B) used w; (C) divided 120 by 6; (D) divided 120 by 12.
The area formula for a triangle is:
Answer: C — A = ½bh
C) Triangle is half of a parallelogram. A) Parallelogram area. B) Twice triangle. D) Adds units that don't make area.
What is the slant height used for in a pyramid?
Answer: C — To find lateral surface area
Slant height is used to calculate the area of each triangular face (lateral face): A = (1/2) × base × slant height. Volume uses perpendicular height, not slant height.
Which angle relationship is illustrated when two parallel lines are cut by a transversal and the angles are on opposite sides of the transversal and between the parallel lines?
Answer: B — Alternate interior angles
Alternate interior angles are between the parallel lines on opposite sides of the transversal; they are congruent. (A) same side, same position; (C) same side, supplementary; (D) formed at one intersection point.
The volume of a triangular prism with triangle base area 10 m² and length 7 m is:
Answer: C — 70 m³
V = base area × length = 10 × 7 = 70 m³. (A) added; (B) used (1/2) × 10 × 7; (D) used (1/4) × 10 × 7.
Area of a trapezoid with parallel sides 5 and 9 and height 4:
Answer: D — 28
D) ½(5+9)(4) = ½·14·4 = 28. A) Forgot ½. C) ½·9·4. B) ½·14·2.
4 cards from the 17 in this chapter.
Triangle inequality?
Sum of any two sides must be greater than the third.
Find area of a trapezoid: bases 6 and 10, height 4.
32 sq units. ((6+10)/2 × 4 = 8 × 4 = 32.)
What is the formula for area of a trapezoid?
A = (1/2)(b₁ + b₂)h.
Find the volume of a cylinder with radius 3 and height 5. (Use π ≈ 3.14)
≈ 141.3 cubic units. (3.14 × 9 × 5.)
These are a sample. The full Area, Surface Area, and Volume in Real-World Problems chapter runs 54 items with per-chapter progress tracking, on the web and in the iOS app.
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