Engineering Graphics

1. 20MEGO1
Engineering
Graphics
Preparedby:
M. Sundra Pandian, M.E., M.B.A.
Assistant Professor, Department of Mechanical Engineering,
Sri Ramakrishna Institute of Technology, Coimbatore - 10
Module 3

2. Syllabus
Projection of Solids (Module 3)
Projection of simple solids like prisms, pyramids, cylinder,
cone and truncated solids when the axis is inclined to one of the
principal planes by rotating object method and auxiliary plane
method.

3. Introduction
Definition
Solids are 3 dimensional figures with length, width and
thickness or height.

4. Face
Generator
Base
or
End
Apex
Vertex
Terminology
The below are some common terms used in solids.

5. Types
a. Polyhedron
A polyhedron is defined as a solid bounded by planes called
faces. When all faces are equal and regular, the polyhedron is said to
be regular.
b. Solids of Revolution
The solids generated by revolving any segment around an
axis is called solids of revolution.

6. Polyhedron - 7 Types
1. Tetrahedron
Four faces – All are equilateral triangles.
2. Hexahedron or Cube
Six faces – All squares – Cube
Six faces – All Rectangles or Rectangles and Squares – Cuboid
Six Faces – All faces are Parallelograms – Parallelopiped

7. Polyhedron
3. Octahedron
Eight faces – All are equal equilateral triangles.
4. Dodecahedron
12 faces – All Pentagons
5. Icasohedron
20 faces – All equal equilateral triangles

8. Polyhedron
6. Prism
This is a polyhedron having two equal and similar faces called its ends
or bases, parallel to each other and joined by other faces which are
parallelograms. The imaginary line joining the centers of the bases is called the
axis.
A right and regular prism has its axis perpendicular to the
bases. All its faces are equal rectangles.

9. Polyhedron
6. Prism

10. Polyhedron
7. Pyramids
This is a polyhedron having a plane figure as a base and a number of
triangular faces meeting at a point called the vertex or apex. The imaginary
line joining the apex with the center of the base is its axis.
A right and regular pyramid has its axis perpendicular to the base
which is a regular plane figure. Its faces are all equal isosceles triangles.
Oblique prisms and pyramids have their axes inclined to their bases.
Prisms and pyramids are named according to the shape of their bases, as
triangular, square, pentagonal, hexagonal etc.

11. Polyhedron
7. Pyramid

12. Solids of Revolution
1. Cylinders
A right circular cylinder is a solid generated by the revolution of a
rectangle about one of its sides which remains fixed.
It has two equal circular bases. The line joining the centers of the bases
is the axis. It is perpendicular to the bases.

13. Solids of Revolution
2. Cone
A right circular cone is a solid generated by the revolution of a
right-angled triangle about one of its perpendicular sides which is fixed.
3. Sphere
A sphere is a solid generated by the revolution of a semi-circle about
its diameter as the axis. The mid-point of the diameter is the center of the
sphere. All points on the surface of the sphere are equidistant from its center.

14. Solids of Revolution
4. Frustums
When a pyramid or a cone is cut by a plane parallel to its base,
thus removing the top portion, the remaining portion is called its frustum
5. TruncatedSolids
When a solid is cut by a plane inclined to the base it is said to be
truncated.

15. Projections of Solids
Axis Perpendicular to One plane
x
y

16. g’
c’
Projection of Solids – Axis Perpendicular to H.P
Draw the projection of a equilateral triangular prism of base side
20mm and height of the axis 60 mm, having its base on the HP and axis
perpendicular to HP and one of its base side is parallel to VP.
x y
20
a (e) b (f)
60°
c (g)
o
60
a’ b’
e’ f ’
F.V
F.V
T.V
T.V
A
B
C
E
F
G

17. Draw the projection of a square pyramid of side 30 mm and height 65
mm resting on VP and one of its base edge is perpendicular to HP.
x y
a’ b’
c’
d’
o’
d(a) c(b)
o
30
65
Projection of Solids – Axis Perpendicular to V.P

18. A cube of 50 mm long edges is resting on HP with its vertical faces
equally inclined to the V.P. Draw the projections.
Projection of Solids
x
y
45°
45°

19. A cube of 50 mm long edges is resting on HP with its vertical faces
equally inclined to the V.P. Draw the projections.
x y
Projection of Solids
45°
a (e)
b (f)
c (g)
d (h)
50
a’ b’ (d’) c’
e’ f’ (h’) g’

20. A hexagonal prism of base side 30 mm and height 60 mm is resting
on the VP with its axis and one of the base side parallel to HP. Draw its
projections.
x y
Projection of Solids
a’ b’
c’
d’
e’
f’ o’
60
(a) (b) c
d
e
f

21. Draw the projections of a pentagonal pyramid, base 30 mm side and
axis 60 mm long, having its base on the H.P. and one of the edges of the base
inclined at 45° to the V.P.
x y
Projection of Solids
45°
a
b c
d
e
o
a’
b’ c’
d’
e’
o’
60

22. 21
a1
e’
Draw the projections of a pentagonal prism, base edge 35 mm and
height 70 mm long, resting on HP with one of its corners touching the HP. Its
axis is inclined at an angle of 30° to HP and parallel to VP.
x y
Axis Parallel to one plane and Inclinedto another
a(1) b(2)
c(3)
d(4)
e(5)
0
35
70
a’ b’ c’
d’
Note: If axis
inclination angle
is given, draw the
base with an
inclination of
(90° - Axis angle)
60°
a1’
b1’
c1’
d1’
e1’
1’ 2’ 3’
4’
5’
11’
21’
31’
41’
51’
b1
c1
d1
e1
11
31
41
51

23. 45°
f1
f
Draw the projections of a hexagonal pyramid, base edge 35 mm and
height 70 mm long, resting on VP with one of its base corner touching the VP
and axis inclined at an angle of 45° to VP and parallel to HP.
x y
Axis Parallel to one plane and Inclinedto another
a’ b’
c’
d’
e’
f’ o’
(a) e (b) d c
o
70
(a1) e1
(b1)d1
c1
o1
01
’
a1
’ b1
’
c1
’
d1
’
e1
’
f1
’
Method 1: Rotating Object Method

24. 45°
a1
f
y
Axis Parallel to one plane and Inclinedto another
a’
b’
c’
d’
e’
f’ o’
(a) e (b) d c
o
70
Method 2: Auxiliary Plane Method
x1
y1
Note:
• Measure a’ from
xy ref. line.
• Draw an arc with
radius as this
distance from
new ref. line x1-y1
• This arc cuts the
projector through
a at a1.
b1
c1
d1
e1
f1
o1

25. 61’
31’
a1’
Draw the projections of a cylinder of base diameter 50 mm and height
65 mm resting on HP on one of its generators with axis parallel to HP and
inclined at 30° to VP.
x y
Axis Parallel to one plane and Inclinedto another
ø50 a’(1’)
b’(2’) d’(4’)
e’(5’)
f ’(6’)
g’(7’)
h’(8’)
o’
65
a
(b)h (c)g (d)f e
60° 30°
a1
(b1)h1
(c1)g1
(d1)f1
e1
11
(31)71
(41)61
51
b1’
c1’
d1’
e1’
f1’
g1’
h1’
11’
21’ 41’
51’
71’
81’

26. b 1
Draw the projections of a right circular cone of base diameter 60 mm
and height 80 mm resting on HP on one of its generators with axis parallel to
VP.
x y
Axis Parallel to one plane and Inclinedto another
a
b
c
d
e
f
g
h
ø60
o
a’
(b’)h’ (c’)g’ (d’)f’
e’
80
o’
Generator
e1’ o1’
a1’
(b1’) h1’
(c1’) g1’
(d1’) f1’
o1
a1
c 1
d 1
e 1
f 1
g 1
h 1

27. a1’(b1’) 60°
Draw the projections of a tetrahedron of base side 50 mm resting on
HP on one of its edge and that edge is perpendicular to VP. The axis is inclined
at 30° to HP.
x y
Axis Parallel to one plane and Inclinedto another
a
b
50 c
o
h = a(2/3)
o’
a’(b’) c’
c1’
o1’
a1
b1
c1
o1

28. Draw the projections of a rectangular pyramid, of base
40 mm X 30 mm and height 60 mm resting on VP on its base. A corner of the
base is touching the HP and the longer side containing that corner is inclined
at 30° to HP. The axis is perpendicular to VP.
x y
Axis Parallel to one plane and Inclinedto another
30°
a’
b’
c’
d’ o’
a b
c
d
60
o

29. 60°
Draw the projections of a right cylinder of base diameter 50 mm and
height 65 mm resting on HP on one of its base points with axis inclined at 30°
to HP and 45 ° to VP.
x y
Axis Inclined to both planes
a
b
c
d
e
f
g
h
o
Ø 50
65
a’ c’(g’) d’(f’)
1’
3’(7’)
5’ 1 1’
5 1’
31’(71’)
a 1’
e 1’
c1’(g1’)
45°

30. b1
d1’
30°
Draw the projections of a pentagonal pyramid of base edge 30 mm
and height 70 mm resting on HP on one of its base corner with axis inclined at
60° to HP and 30 ° to VP.
x y
Axis Inclined to both planes
a
b c
d
e
30
o
a’
b’ c’
d’
e’
70
o’
a1’
90°
o1’
b1’
c1’
e1’
a1
c1
d1
e1
o1
60°
a2
b2
c2
d2
e2
o2
a2’
b2’
c2’
d2’
e2’
o2’

31. A solid might be cut and the cut solid is then projected on the
HP and VP as per the conditions of the position of the solid.
The plane which is cutting the solid is known as Cutting
Plane or Section Plane (S.P) and is denoted as follows.
Sections of Solids
S P

32. Draw the projections of a triangular pyramid of base edge 40 mm and
height 60 mm resting on HP on its base, with one of its base edge parallel to
VP. It is cut by a plane inclined at 30° to HP and cutting the axis of the
pyramid 45 mm from the base. Draw its projection ad the true section.
Section of Solids

33. 21’
1’
2’
80
x y
Section of Solids
40
a
b
c
o
a’
b’
c’
45
o’
30°
3’
1 3
2
Note:
1. Measure 1 from x-y.
2. Mark 11’ along 1’
above x1 – y1.
x1
y1
11’
31’
True Shape of
Section (T. S)

34. Draw the projections of a rectangular prism of base 50 mm X 40 mm
and height 70 mm resting on HP on its base, with one of its longer edge of the
base parallel to VP. It is cut by a plane inclined at 45° to HP and passing
through the mid-axis. Draw its projection ad the true section.
Section of Solids

35. 90°
b’(c’) y
Section of Solids
50
40
x
a b
c
d
a’(d’)
70
35
o
45°
1’(4’)
2’(3’)
x1
y1
Note:
1. Measure 1 from x-y.
2. Mark 11’ along 1’ above x1 – y1.
11’
21’
31’
41’
T.S of Section

36. Syllabus
Projection of Solids (Module 3)
Projection of simple solids like prisms, pyramids, cylinder,
cone and truncated solids when the axis is inclined to one of the
principal planes by rotating object method and auxiliary plane
method.