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20 multiple-choice questions and 15 flashcards on Circumference and Area of Circles, about 13% of the 7th Math: Geometry bank. Every one carries a written rationale.
Circumference and Area of Circles is one of 6 chapters in CoStudy's 7th Math: Geometry bank, and it holds 20 of the bank's 150 multiple-choice questions — roughly 13% 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.
5 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.
A garden is drawn at 1:20 scale. The drawing shows 5 cm × 8 cm. Actual area?
Answer: C — 16,000 cm²
Actual dims: 5×20 = 100 cm; 8×20 = 160 cm; area = 100 × 160 = 16,000 cm². (A) forgot scale; (B) multiplied area by 20 once instead of 20²; (D) converted to m² incorrectly.
A map has scale 1 inch = 50 miles. Two cities are 3.5 inches apart on the map. Actual distance?
Answer: C — 175 miles
3.5 × 50 = 175 miles. (A) used 2 × 50; (B) used 3 × 50; (D) used 4 × 50.
Find the area of a circle with diameter 10 (π ≈ 3.14).
Answer: D — 78.5
D) Radius = d/2 = 5; A = πr² = 3.14·25 = 78.5. A) Used d (10) as r so A = π·100. C) Used circumference 2πr = 31.4. B) Forgot π and used r² = 25.
If a circle's radius doubles, the area becomes:
Answer: D — 4× larger
D) A = πr²; doubling r multiplies area by 2² = 4. A) Linear scaling only. B) Area changes. C) That's volume scaling (cubed).
A triangle has angles 55° and 70°. The third angle is:
Answer: B — 55°
55 + 70 + x = 180 → x = 55°. (A) arithmetic error; (C) arithmetic; (D) subtracted from 180 incorrectly.
4 cards from the 15 in this chapter.
Cross-section of a cube parallel to a face is?
A square (the same size as the face).
Volume of cylinder?
V = πr²h.
What is 'pi' (π)?
The ratio of a circle's circumference to its diameter. Approximately 3.14159...
Find the circumference of a circle with radius 5. (Use π ≈ 3.14)
31.4 units. (2 × 3.14 × 5.)
These are a sample. The full Circumference and Area of Circles chapter runs 35 items with per-chapter progress tracking, on the web and in the iOS app.
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