Sections of Solids Questions and Answers

Answer: A

Correct answer: both the assertion and the reason are true and the reason explains the assertion

Both are true and the reason gives the mechanism. Every point of the surface lies at the radius from the centre, so the points lying in a given plane are all at a fixed distance from the foot of the perpendicular from the centre to that plane - which is the definition of a circle in that plane.

Answer: B

Correct answer: both the assertion and the reason are false, the section being similar but smaller

Neither statement holds. The section of a pyramid parallel to its base is similar to the base but reduced by the ratio of the heights, so it is not identical. And parallel planes cut a solid in congruent figures only where the solid has a constant cross-section, as a prism or cylinder does - not a pyramid or cone.

Answer: C

Correct answer: an ellipse for every oblique cut clear of the bases

The cylinder’s generators are parallel, so any oblique plane crossing them all meets every one and the section always closes into an ellipse. A cone’s generators converge, so a plane may fail to meet some of them, and that is what produces the parabola and hyperbola which a cylinder cannot give.

Answer: D

Correct answer: a view projected on a plane parallel to the cut

A face appears at true size only when the plane of projection is parallel to it, which is the whole principle of the auxiliary view. A section inclined to both principal planes is foreshortened in the plan and in the elevation alike, so a third plane must be set parallel to the cut.