Question 1

Curve of intersection — When a plane cuts a circular cylinder (not a cone), is the resulting curve correctly named a “conic section,” or should it be described simply as an ellipse/circle produced by a plane–cylinder cut?

Accepted Answer

Introduction / Context: In descriptive geometry, the names of intersection curves matter for precision. “Conic section” has a specific classical meaning: the locus obtained when a plane intersects a cone. A plane intersecting a cylinder can produce a circle or an ellipse, but the naming convention differs from the conic-section definition. Given Data / Assumptions: The statement claims the plane–cylinder intersection is “called a conic section.” We consider a circular right cylinder cut by an arbitrary plane. The observed curve may be a circle (if cut perpendicular to axis) or an ellipse (if cut obliquely but not parallel to generators). Concept / Approach: Although the resulting ellipse is the same geometric shape as one conic type, the term “conic section” refers historically and definitionally to plane–cone intersections. For clarity in drafting/teaching, we typically say “ellipse obtained by cutting a cylinder.” Calling it a conic section blurs the standard classification and source geometry used in many textbooks and standards. Step-by-Step Solution: 1) Recall definition: conic sections arise from plane–cone intersections (circle, ellipse, parabola, hyperbola).2) Recognize the scenario: plane–cylinder intersection produces a circle or ellipse.3) Naming: describe it as “ellipse (or circle) from plane–cylinder intersection,” not a conic section. Verification / Alternative check: Constructive proofs in descriptive geometry derive cylinder–plane ellipses using auxiliary views without invoking cone geometry; pattern development texts maintain the naming distinction for pedagogical consistency. Why Other Options Are Wrong: Correct: Overextends the term “conic section.” Projection-dependent options: The nature of the curve does not depend on orthographic vs pictorial projection. “Depends on obliquity”: Obliquity changes whether the curve is a circle or ellipse, not the classification as a conic section. Common Pitfalls: Assuming any ellipse must be a “conic section” by name; forgetting that definitions link shapes to generating solids; mixing classification with visual appearance. Final Answer: Incorrect

Question 2

Classification of solids — Do solids bounded by warped (double-curved, non-developable) surfaces lack a recognized group name in engineering graphics taxonomy?

Accepted Answer

Introduction / Context: Engineering graphics classifies solids to aid communication and manufacturing planning. Common groups include polyhedra, solids of revolution, prisms, pyramids, and bodies formed by translation or sweeping. Surfaces can be developable (flattenable) or non-developable (warped, double-curved). Given Data / Assumptions: Claim: solids bounded by warped surfaces “have no group name.” Warped surfaces include forms like hyperbolic paraboloids and general freeform NURBS patches. Many curricula and texts explicitly group such bodies. Concept / Approach: Solids bounded primarily by warped (double-curved) surfaces are commonly grouped as warped solids or freeform solids in drafting pedagogy. While their geometry can be diverse, the group label serves practical classification distinct from polyhedra (planar faces) and solids of revolution (generated by rotating a profile). Therefore, the assertion that no group name exists is incorrect. Step-by-Step Solution: 1) Identify the surface type: warped (non-developable) with curvature in two principal directions.2) Check taxonomy: educational references list “warped solids/freeform solids.”3) Conclude the statement is false; a group label exists. Verification / Alternative check: CAD libraries segregate primitives and freeform/lofted/ruled surfaces; curricula often divide solids into polyhedra, revolution, and warped/freeform groups, confirming the naming practice. Why Other Options Are Wrong: Correct: Contradicts widespread taxonomy. They are polyhedra / always solids of revolution: Both require planar faces or rotational generation, which warped solids lack. Unclassifiable: Practical labels exist for instruction and documentation. Common Pitfalls: Thinking “no single formula” means “no category”; assuming only primitives deserve group names; conflating “complex” with “unclassifiable.” Final Answer: Incorrect

Question 3

Primary auxiliary view rule — Must a primary auxiliary view be constructed on a plane parallel to the associated inclined surface to show its true size/shape?

Accepted Answer

Introduction / Context: Auxiliary views are created to project an inclined or skewed feature onto a plane where it appears true size and true shape. The orientation of the projection plane relative to the feature determines whether foreshortening vanishes. Given Data / Assumptions: Claim: a primary auxiliary “does not need” to be parallel to the inclined plane. Primary auxiliary view is the first auxiliary taken directly from a principal view. Objective: obtain true geometry of the chosen surface/edge. Concept / Approach: To remove foreshortening of a plane, project it onto a plane that is parallel to it. A primary auxiliary view is constructed with the auxiliary plane parallel to the inclined surface (and perpendicular to the projection direction). If the plane is not parallel, the feature remains foreshortened and the purpose is defeated. Step-by-Step Solution: 1) Identify the inclined surface whose true shape is required.2) Place the auxiliary plane parallel to that surface.3) Project perpendicular to the auxiliary plane to obtain true size/shape.4) Therefore the statement is false. Verification / Alternative check: Demonstrate with a rectangular plate inclined to the frontal plane: only when the auxiliary plane is parallel to the plate does the outline appear as a true rectangle; any other orientation yields foreshortening. Why Other Options Are Wrong: Correct: Contradicts projection theory. Only necessary for secondary auxiliaries: Both primary and secondary follow parallelism rules to achieve true views. Depends on rotation angle: Rotation is chosen to achieve parallelism, not to avoid it. True only for cabinet oblique drawings: Oblique pictorials are unrelated to orthographic auxiliary construction. Common Pitfalls: Forgetting which plane must be parallel; mixing auxiliary with pictorial methods; attempting to “eyeball” true shape without establishing correct projection geometry. Final Answer: Incorrect

Auxiliary Views Questions