Eg unit 4

20MEGO1 Engineering Graphics
Prepared by:
M. Sundra Pandian, M.E., M.B.A.
Assistant Professor, Department of Mechanical Engineering,
Sri Ramakrishna Institute of Technology, Coimbatore - 10
Module 4

Projection of Sectioned Solids and Development of Surfaces
(Module 4)
Sectioning of above solids in simple vertical position when
the cutting plane is inclined to the one of the principal planes and
perpendicular to the other – obtaining true shape of section.
Development of lateral surfaces of simple and sectioned solids –
Prisms, pyramids, cylinder and cone. Development of lateral surfaces
of solids with cut-outs and holes.
Syllabus

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.
S P
Sections of Solids

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 at 45 mm from the base. Draw its
projection ad the true section.
Section of Solids

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)

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 mid-axis. Draw its
projection and the true section.
Section of Solids

90°
b’(c’) y
Section of Solids
50
40
x
1(a) 2(b)
3(c)
4(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.
41’
31’
21’
11’
T.S of Section

A cube of side 30 mm rests on the HP on its end with the
vertical faces equally inclined to the VP. It is cut by a plane
perpendicular to the VP and inclined at 30° to HP meeting the axis
at 25 mm above the base. Draw its front view, sectional top view
and true shape of the section.
Section of Solids

30°
2’
11’
45°
Section of Solids
y
x
 30
(a)
(b)
(c)
(d)
o
30
a’ b’(d’) c’
25
1’
3’(4’)
(5’)
1
2
3
5
x1
y1
21’ 31’
41’
51’
4
T.S

A cylinder of diameter 50mm and height 60mm rests on its
base on H.P. It is cut by a plane perpendicular to V.P. and inclined
at 45° to H.P. The cutting plane meets the axis at a distance of
15mm from the top. Draw the sectional plan and true shape of the
section.
Section of Solids

45°
3’
Section of Solids
y
x
ø50 (a)
(b) (c)
(d)
(e)
(f)
(g)
(h)
o
60
a’ b’(h’) c’(g’) d’(f’) e’
15
1’
2’
4’
(5’)
(6’)
(7’)
1
2 3 4
5
6
7
11’
21’
31’ 41’
51’
61’
71’
T.S

A cone of base diameter 50mm and altitude 50mm rests on its
base on the HP . It is cut by a plane perpendicular to the VP and
parallel to one of the extreme generators , 10mm away from it .Draw
the sectional top view and the true shape of the section.
Section of Solids

Section of Solids
y
x
ø50 (a)
(b) (c)
(d)
(e)
(f)
(g)
(h)
o
a’ b’(h’) c’(g’) e’
50
o’
10
1’
2’
3’
4’ 5’
(6’)
(7’)
1
2
7
3
6
4
5
11’ 21’ 31’
41’
51’
61’
71’ T.S

Imagine that a solid is enclosed in a wrapper of thin
material, such as paper.
If this covering is opened out and laid on a flat plane, the
flattened-out paper is the development of the solid.
Thus, when surfaces of a solid are laid out on a plane, the
figure obtained is called its development.
Development of Surfaces

i) Parallel Line Development
Methods of Development of Surfaces
ii) Radial Line Development

Methods of Development of Surfaces

Exercise:
A rectangular prism of base side 40 mm x 30 mm and axis height
60 mm is resting on its base on HP with two of its lateral surfaces parallel to
VP. Draw the development of lateral surfaces of the prism.

A
a’(d’) D
b’(c’)
b
c
d
a
y
x
40
30 o
60
L = 2 (a+b)
L = 2 (40+30) = 140
B C A
60
Note: The no. of vertical faces (pink rectangles will be
equal to the no. of sides on the prism base.

Exercise:
A right circular cylinder of base diameter 40 mm and axis height
60 mm is resting on its base on HP on its base. Draw the development of
lateral surface.

A
c’ (g’)
y
x
ø40 a
b
c
d
e
f
h
o
60
a’ b’ (h’) d’ (f’) e’
L = 2R
L = 2(40/2) = 62.8
A
B C D E F G H

Exercise:
A square pyramid of base 40 mm and axis height 60 mm is resting
on its base on HP on its base. Draw the development of lateral surfaces of the
pyramid.

B
a’(d’) b’(c’)
y
x
30
a b
c
d
o
60
o’
OX
A
C
D
A
30

Exercise:
A right circular cone of base diameter 40 mm and axis height 60 mm
is resting on its base on HP. Draw the development of lateral surfaces of the
cone..

y
x
c’ (g’)
a
b
c
d
f
h
o
a’ b’ (h’) d’ (f’) e’
ø40
60
o’
O
A
Note:
Radius of base circle , R= 360°
Slant Height, L = 
  = (R/L) * 360
• Divide  into ‘n’ parts as
the no. of parts the circle
is divided into.
°
B
C
D
E
F
G
H
A
L
L

Exercise: A cylinder of diameter 45 mm and height 70 mm is resting vertically
on one of its ends on the HP. It is cut by a plane perpendicular to VP and
inclined at 45º to HP. The plane meets the axis at a point 35 mm above the
base. Draw the development of the lateral surface of the lower portion of the
truncated cylinder.
Development of Lateral Surfaces

45°
1
c’ (g’)
y
x
ø45
A
b
c
d
e
f
h
o
70
a’ b’ (h’) d’ (f’) e’
35
1’
2’
3’
4’
5’
(6’)
(7’)
(8’)
A
L= 2 r = …
70
B C D E F G H
2
3
4
5
6
7
8
1

Exercise: A pentagonal prism of base side 30 mm and axis height 75 mm is
resting on its base on HP with one of its lateral surfaces parallel to VP. It is cut
by plane perpendicular to VP and inclined at 45º to HP, bisecting the axis.
Draw the development of lateral surfaces of the lower portion of the prism.

a
y
x
30
b
c
d
e
70
35
30°
a’ b’ c’
(d’)
(e’)
1’
2’
3’
4’
5’
A A
L= n*a = ….
70
B C D E
1
2
3
4
5
1

Exercise: A hexagonal pyramid of base side 30mm and axis height 60mm is
resting on its base on HP with two of the base edges parallel to VP. It is cut by a
plane perpendicular to VP, inclined 30° to HP and bisects the axis of the
pyramid. Draw the development of the lateral surfaces of the lower portion of
the pyramid.

LA
1
B
y
x
30
a
b c
d
e
f
o
60
a’ b’(f’) c’(e’) d’
o’
30
30°
1’
2’
3’
4’
(5’)
(6’)
L
O
LB
LC
LD
L
A
30
C
D
E
F
A
LA
1
LA
2
LB
6
LF = LB
3
LC
5
LE = LC
4 LC

Exercise: A right circular cylinder of diameter 40 mm and height 60 mm is
resting on the H.P on its base. A 20 mm square hole is cut on mid-axis of the
cylinder whose sides are equally inclined to H.P. Draw the development of the
lateral surface.

1
Note:
360° = 2 r &  = x
 x = ( X 2 r) / 360°
o
c’ (g’)
y
x
ø40
b
c
d
e
f
h
60
a’ b’ (h’) d’ (f’) e’
30
a
1’
2’
3’
4’
1
2 & 4
3

L= 2 r = …
A A
B C D E F G H
x
2
3
4

Exercise: A right circular cone of diameter 40 mm and height 60 mm is resting
on the H.P on its base. A 20 mm diameter hole is cut at 18 mm from the base
on the curved surface. Draw the development of the lateral surface.

2
y
x
c’ (g’)
a
b
c
d
f
h
o
a’ b’ (h’) d’ (f’) e’
ø40
60
o’
O
A
Note:
 = (R/L) * 360
°
B
C
D
E
F
G
H
A
L
L
18
1’
2’
3’
4’
L1
L2
L3
L4 L1
1
L2
L3
L4
3
4

Eg unit 4

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