What distinguishes the true shape of a section from its apparent shape in a principal view?
Answer: A
A section plane inclined to a principal plane is seen obliquely in that view, so the cut appears foreshortened there. Projecting onto a plane parallel to the section plane, which means perpendicular to the direction of view along it, restores the figure to its true size and shape.
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Where must an auxiliary plane be placed to reveal the true shape of a cut?
Answer: B
Parallelism between the auxiliary plane and the cutting plane is what removes the foreshortening in every direction at once. Setting the auxiliary perpendicular to the section plane instead would reduce the whole cut surface to a single straight line.
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How does a section plane perpendicular to the vertical plane appear in the elevation?
Answer: C
Being perpendicular to that plane, the cutting plane is seen edge on from the front and collapses to a line, which is why the section plane is normally set in that position. Its inclination in the elevation then gives the angle of the cut directly.
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Which part of the solid is retained and drawn in a sectional view?
Answer: D
The near portion is imagined removed so that the interior is exposed, and the arrows on the cutting plane line record the direction of viewing. Retaining the wrong half is a frequent error and produces a view that contradicts the arrows.
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How is the cut surface distinguished in a sectional view?
Answer: A
Evenly spaced thin lines at forty-five degrees mark the material actually cut through, so the cut face reads unmistakably against the surfaces merely seen beyond it. Very thin sections are the recognised exception and may be filled solid.
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Cutting a vertical square prism by a plane parallel to its base produces a section that is
Answer: B
Correct answer: a square identical to the base
A prism has a constant cross-section along its length, so any plane parallel to the base cuts it in exactly the same figure. The height at which the cut is made makes no difference - which is what distinguishes a prism from a pyramid, where the section shrinks as the cut rises.
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Cutting a vertical square prism by a plane inclined to its base gives a section whose shape is
Answer: C
Correct answer: a rectangle longer than the base in one direction
The cut still crosses the same two pairs of faces, so the figure remains a rectangle; but the distance between the two faces it crosses obliquely is stretched by the inclination, while the other pair is unaffected. One dimension of the base is therefore preserved and the other lengthened.
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Cutting a pyramid by a plane parallel to its base yields a figure that is
Answer: D
Correct answer: similar to the base but smaller
The faces of a pyramid converge towards the apex, so a plane parallel to the base cuts a figure of the same shape scaled down by the ratio of the heights. The two figures are similar rather than congruent, and the area ratio is the square of that scale factor.
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What section results when a plane passes through the apex of a pyramid and across its base?
Answer: A
Correct answer: a triangle
A plane through the apex meets the sloping surface in two straight generators and the base in a straight line, so the boundary consists of three straight segments. This is the one cut of a cone or pyramid that produces no curve at all, however the plane is turned about the apex.
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A pyramid is cut by a plane inclined to the base and meeting all its lateral edges. The section has
Answer: B
Each lateral face contributes one straight edge to the cut, so a hexagonal pyramid cut across all six faces gives a hexagonal section. The section is not similar to the base, since the edges are cut at differing distances from the apex.
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