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18 multiple-choice questions and 12 flashcards on Cross-Sections of Three-Dimensional Figures, about 12% of the 7th Math: Geometry bank. Every one carries a written rationale.
Cross-Sections of Three-Dimensional Figures is one of 6 chapters in CoStudy's 7th Math: Geometry bank, and it holds 18 of the bank's 150 multiple-choice questions — roughly 12% 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.
9 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 slice parallel to the base of a square pyramid produces:
Answer: B — Smaller square (similar to base)
B) Cross-sections parallel to base are similar to the base — a smaller square. A) Through apex. C/D) Wrong shapes.
The circumference of a circle with diameter 10 cm is approximately: (Use π ≈ 3.14)
Answer: A — 31.4 cm
C = πd = 3.14 × 10 = 31.4 cm. (B) used C = πd² ; (C) used area formula A = πr²; (D) used C = πr.
The sum of interior angles of a triangle is:
Answer: B — 180°
All triangles have interior angles summing to 180°. (A) is a right angle; (C) is a quadrilateral; (D) not a polygon angle sum.
A circle has circumference 25.12 cm. Its radius is approximately: (π ≈ 3.14)
Answer: D — 4 cm
r = C/(2π) = 25.12/(6.28) = 4 cm. (A) used diameter as radius; (C) confused diameter and radius; (B) halved C without dividing by π.
An oblique (tilted) slice through a cylinder gives:
Answer: C — Ellipse
C) Tilted cut → ellipse. A) Only perpendicular cuts. B) Only axial cuts. D) Not possible.
A vertical slice through the apex of a cone (containing the axis) gives:
Answer: B — Triangle
B) The axis-containing cut shows a triangular profile. A) Only for horizontal cuts. C/D) Wrong shape.
Two angles are supplementary. One measures 65°. The other measures:
Answer: D — 115°
Supplementary angles sum to 180°: 180 − 65 = 115°. (A) complementary to 65°; (C) arithmetic error; (B) subtracted from 360°.
The cross-section of a horizontal cut through a cylinder is:
Answer: B — A circle
B) Slicing parallel to the bases of a right cylinder reveals the circular base. A) Only for tilted cuts. C/D) Wrong base shape.
Vertical angles are:
Answer: B — always equal
Vertical angles are formed by two intersecting lines and are always congruent (equal). (A) supplementary = 180°; (C) complementary = 90°; (D) they are opposite, not adjacent.
3 cards from the 12 in this chapter.
Vertical angles formed by two intersecting lines are?
Equal (congruent).
Cross section of a cone cut horizontally?
A circle (smaller than the base).
What is a 'cross section' of a 3D figure?
The 2D shape made when you slice through the 3D figure.
These are a sample. The full Cross-Sections of Three-Dimensional Figures chapter runs 30 items with per-chapter progress tracking, on the web and in the iOS app.
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