This set of Engineering Drawing Multiple Choice Questions & Answers (MCQs) focuses on “Development of Simple Solids”.

1. Which of the following surfaces can be developed accurately?

a) Double-curved surfaces

b) Spheres

c) Warped surfaces

d) Polyhedra

View Answer

Explanation: A smooth surface with zero Gaussian curvature is theoretically considered as developable surfaces as they are considered as the surfaces that can be developed without error. Polyhedra are 3-D solids which can be easily developed.

2. In which of the following methods, stretch-out-line principle is used?

a) Approximate development

b) Parallel line development

c) Triangulation method

d) Radial line development

View Answer

Explanation: In the parallel line development method a surface is divided into a series of parts by parallel lines, which can help us in identifying the shape. Drawing stretch-out lines is one of the steps in this process.

3. What is the shape of the development of the lateral surface of the cylinder?

a) A rectangle with length equal to the circumference of the base circle, and breadth equal to the height of the cylinder

b) A rectangle with length equal to the diameter of the base circle, and breadth equal to the height of the cylinder

c) A square with the length of the sides equal to the height of the cylinder

d) A rectangle with length equal to the circumference of the base circle, and breadth equal to the diameter of the base circle

View Answer

Explanation: In the case of a cylinder, the lateral surface when developed takes the shape of a rectangle with length equal to the circumference of the base circle and breadth equal to the height of the cylinder.

4. In the case of the cones, what is the value of the radius of the arc in the development of surface?

a) Radius

b) Height

c) Slant height

d) 0.5 times the slant height

View Answer

Explanation: The true length of the slant height is taken as the radius for the development of surfaces of cones. An arc is drawn with the appropriate included angle.

5. What is the subtended angle value for the sector used in the development of the cone?

a) 360° X \(\frac{radius \, of \, circular \, base}{height}\)

b) 360° X \(\frac{circumference \, of \, circular \, base}{slant \, height}\)

c) 360° X \(\frac{radius \, of \, circular \, base}{slant \, height}\)

d) 360° X \(\frac{diameter \, of \, circular \, base}{slant \, height}\)

View Answer

Explanation: In the development of the surface of the cone, an arc with an included angle equal to the \(\frac{base \, circle \, circumference}{slant \, height}\) radians when converted to degrees it is equal to 360° X \(\frac{radius \, of \, circular \, base}{slant \, height}\).

6. A hollow cylinder with negligible thickness, height 10 cm, and base circle with radius 5 cm. Find the area of the surface developed?

a) 344.3 cm^{2}

b) 314.3 cm^{2}

c) 214.3 cm^{2}

d) 244.3 cm^{2}

View Answer

Explanation: The lateral surface when developed takes the shape of a rectangle with length equal to the circumference of the base circle and breadth equal to the height of the cylinder, hence the area is equal to 2

*Π*r*h. Hence it is equal to 314.3 cm

^{2}.

7. What is the value of slant height value for a cone of radius r, and height of the cone is h?

a) (r^{2}+h^{2})^{2}

b) (r^{2}-h^{2})^{0.5}

c) (h^{2}-r^{2})^{2}

d) (r^{2}+h^{2})^{0.5}

View Answer

Explanation: For the surface development of the cone, we need to find the length of the slant height. It is taken as radius and an arc is drawn. As r and h makes a right angle triangle with slant height l as hypotenuse, therefore l = (r

^{2}+h

^{2})

^{0.5}.

8. A cone of radius 3 cm and the height of 4 cm, when its surface is developed forms a sector. What is the value of the included angle of the sector?

a) 120°

b) 205°

c) 216°

d) 112°

View Answer

Explanation: In the development of the surface of the cone, a sector with an included angle equal to 360° X \(\frac{radius \, of \, circular \, base}{slant \, height}\). Slant height value is equal to (r

^{2}+h

^{2})

^{0.5}, as r = 3 cm and h = 4mm, hence slant height is (3

^{2}+4

^{2})

^{0.5}= 5cm. Hence the angle is 360° x \(\frac{3}{5}\)= 216°.

9. What will be the value of the radius of the arc in the development of the pyramids?

a) Height of the pyramid

b) The slant height of the pyramid

c) 4*Side of the pyramid

d) 0.5*Height of the pyramid

View Answer

Explanation: In the process of surface development of the pyramid, we use the radial line method where we take the true length of the slant height is taken as the radius and an arc is drawn.

10. In the process of development of pyramids, the method used is ______

a) Triangulation development

b) Parallel line development

c) Approximate development

d) Radial line development

View Answer

Explanation: The true length of a cone generator is taken as the radius and the surface of the pyramid is developed. This is what we do in the radial line development method.

11. In the surface development of pyramids, using the rotation method slant height true length is measured.

a) True

b) False

View Answer

Explanation: In the surface development of pyramids directly measuring the slant height may give the wrong values as it is inclined to both H.P and V.P. hence using the rotation method we need to find the value of slant height.

12. What do folding the following sheet results in?

a) Cylinder

b) Cube

c) Square prism

d) Square pyramid

View Answer

Explanation: The given sheet shape is the result of surface development using the parallel line method. Folding the sheet above gives a square prism.

13. A cone of radius 3 cm and the slant height of 12 cm, when its surface is developed forms a sector. What is the value of the included angle of the sector?

a) 120°

b) 90°

c) 75°

d) 112°

View Answer

Explanation: In the development of the surface of the cone, a sector with an included angle equal to 360° X \(\frac{radius \, of \, circular \, base}{slant \, height}\). Hence the value of the angle is 90°.

14. When the ______________ is surface developed the following shape is created.

a) Cone

b) Square pyramid

c) Triangular pyramid

d) Triangular prism

View Answer

Explanation: In the development of the triangular pyramid, the above shape is created. The above diagram has the features of the triangular development of surfaces.

15. What is the actual 3D shape of the following surface development sheet?

a) Cylinder

b) Cone

c) Square pyramid

d) Square prism

View Answer

Explanation: The given shape represents the shape of a cylinder when folded. The above diagram has the features of parallel-line development of surfaces.

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