This set of Civil Engineering Drawing Multiple Choice Questions & Answers (MCQs) focuses on “Intersection of Surfaces”.

1. The red, blue curve in the figure (shown below) represents_____

a) welding

b) joining

c) fitting

d) curve of intersection

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Explanation: Whenever two or more solids combine, a definite curve is seen at their intersection. This curve is called the curve of intersection (COI). Lines of intersection are a common feature in engineering applications or products. Figure 1 shows few examples of intersection lines frequently observed in chemical plants, domestic appliances, pipe joints, etc. Curves of intersections are important from the point of view of production of components for engineering applications.

2. A cylinder of 80 mm diameter and 100 mm axis is completely penetrated by a cone of 80 mm diameter and 120 mm long axis horizontally. Both axes intersect & bisect each other. What will be its top view?

a) Triangle with a circle

b) Cylinder with a triangle

c) Cylinder with a circle

d) Circle with a cylinder

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3. A cylinder 50mm dia. and 70mm axis is completely penetrated by a triangular prism of 45 mm sides and 70 mm axis, horizontally. One flat face of prism is parallel to Vp and Contains axis of cylinder. Draw projections showing curves of intersections.

a) Triangle with a circle

b) Cylinder with a triangle

c) Cylinder with a circle

d) Circle with a cylinder

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4. Find the equation of the intersection of the surface z=4-y2 with the x-y plane.

a) y=2

b) y=+3, y=-3

c) y=+4, y=-4

d) y=+2, y=-2

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Explanation: Set z=0 in the equation, you get 0=4-y2. That simplifies to y2=4, or y= ±2, i.e. two lines: y=2 and y=-2.

5. The________ planes are so selected as to cut the surface of one of the solids in straight lines and that of the other in straight lines or circles.

a) line

b) cutting

c) horizontal

d) xy

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Explanation: Line method: A number of lines are drawn on the lateral surface of one of the solids and in the region of the line of intersection. Points of intersection of these lines with the surface of the other solid are then located. These points will lie on the required line of intersection. They are more easily located from the view in which the lateral surface of the second solid appears edgewise (i.e. as a line). The curve drawn through these points will be the line of intersection.

Cutting-plane method: The two solids are assumed to be cut by a series of cutting planes. The cutting planes may be vertical (i.e. perpendicular to the H.P.), edgewise (i.e. perpendicular to the V.P.) or oblique. The cutting planes are so selected as to cut the surface of one of the solids in straight lines and that of the other in straight lines or circles.

6. In the following figure which figure represents intersection of a sphere and a cylinder touching in a singular curve?

a)

b)

c)

d)

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Explanation: It is an easy task to determine the intersection points of a line with a quadric one only has to solve a quadratic equation. So, any intersection curve of a cone or a cylinder (they are generated by lines) with a quadric consists of intersection points of lines and the quadric (see pictures).

The pictures show the possibilities which occur when intersecting a cylinder and a sphere:

1. In the first case, there exists just one intersection curve.

2. The second case shows an example where the intersection curve consists of two parts.

3. In the third case, the sphere and cylinder touch each other at one singular point. The intersection curve is self-intersecting.

4. If the cylinder and sphere have the same radius and the midpoint of the sphere is located on the axis of the cylinder, then the intersection curve consists of singular points (a circle) only.

7. The figure represents the intersection of two __________

a) concentric spheres

b) swimming flotation

c) tori

d) rings

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Explanation: The intersection curve of two polyhedrons is a polygon i.e. tori. The display of a parametrically defined surface is usually done by mapping a rectangular net into 3-space. The spatial quadrangles are nearly flat. So, for the intersection of two parametrically defined surfaces, the algorithm for the intersection of two polyhedrons can be used.

8. The figure below represents the________ view of the pentagonal base joined to a circular top.

a) side

b) front

c) top

d) bottom

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Explanation: Figure 1 shows the top view and pictorial view of two transition pieces: (a) the pentagonal base joined to a circular top and (b) circular base connected to a square top. The lateral surface of the transition piece must be divided in to curved and non-curved triangles as shown in figure 1.Divide the curved cross section in to a number of equal parts equal to the number of sides of non-curved cross-section. Division points on the curved cross section are obtained by drawing bisectors of each side of the non-curved cross section. The division points thus obtained when connected to the ends of the respective sides of the non-curved cross-section produces plane triangles. In between two plane triangles there lies a curved triangle. After dividing in to a number of triangles, the development is drawn by triangulation method.

9. The figure (4-sided) below represents the intersection of _________

a) triangular prism standing and Triangular prism penetrating

b) cylindrical prism standing and square prism penetrating

c) sq. prism standing and square prism penetrating

d) triangular prism standing and Square prism penetrating

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10. The figure (4-sided) below represents the intersection of _________

a) triangular prism standing and Triangular prism penetrating

b) cylindrical prism standing and square prism penetrating

c) triangular prism standing and Square prism penetrating

d) cone standing and square prism penetrating

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