Projections of Solids Questions and Answers

Answer: A

Correct answer: an incorrect drawing, the base shape being unobtainable

The staged method exists because the true shape of the base can only be drawn when the base lies parallel to a plane of projection. Attempt the inclined position directly and there is no view in which the base appears at true size, so its outline has to be guessed. Working in stages projects the true shape forward into the inclined position.

Answer: B

Correct answer: a cylinder with its axis vertical

A circular plan with a rectangular elevation is the signature of a cylinder standing on its base: the base circle projects at true size in the plan, and the elevation shows the diameter by the axis length. Lay the cylinder on its side and the two views exchange shapes, a cone would give a triangle, and a sphere a circle in both.

Answer: C

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

Both are true and the reason is the whole of the explanation. Since every orthographic view of a sphere is the same circle of the same diameter, no view contains anything that would change if the sphere were turned, and so nothing on the drawing records an orientation. A sphere has no axis, base or face to fix one.

Answer: D

Correct answer: the assertion is false although the reason offered is a true statement in itself

The reason is true - both the slant height and the vertical height are measured from the apex - but they are measured to different places, the slant height to a point on the base circle and the vertical height to the centre of the base. They are two sides of a right triangle, so the slant height always exceeds the vertical height and can never equal it.

Answer: A

Correct answer: has ends that are similar figures

The parallel cut is what makes the difference. Because a frustum is cut parallel to the base, the section is the same shape as the base and merely smaller, so the two ends are similar figures. A truncated pyramid is cut at an angle, so its section is a different figure and the ends are dissimilar. Both retain no apex, and both can be developed.

Answer: B

Correct answer: the axis of a solid standing on its base

A line projects as a point only when it is perpendicular to the plane of projection, and the plan is projected onto the horizontal plane. The axis of a solid standing on its base is vertical, hence perpendicular to that plane, and so shows as a point. A lateral edge of a pyramid slopes, and the axes in the other two options are horizontal or inclined.