sections of solids engineering graphics unit iv

GE8152
ENGINEERING GRAPHICS
Ravi Sivaprakash AP/MECH AAMEC Kovilvenni

UNIT IV
PROJECTION OF SECTIONED SOLIDS

Definitions
Cutting plane or section plane :
The imaginary plane which is assumed to cut
the object as required is called a cutting
plane or section plane.
Section :
The surface produced when a section plane
cuts a solid is termed a section.

Definitions
Sectional view :
The drawing showing that part of the object
which is between the plane of projection and
the section plane is called a sectional view.
True Shape of Section :
If a solid is sectioned by a section plane and it
is projected to a plane parallel to it, the
shape of the section obtained will be exactly
the section exposed by the section plane.
This shape is called True Shape of Section.

Definitions
Apparent Shape of Section :
If the section plane is inclined to the plane of
projection, the shape obtained will not be
the true shape. Such a shape is called
Apparent Shape of Section.

VP
X
Y
FRONT
VIEW
TOP VIEW
HP
Section Plane
Section
Removed Portion
Retained solid
portion

x y
TRUE SHAPE
Of SECTION
SECTION
PLANE
SECTION LINES
(450
to XY)
Apparent Shape
of section
SECTIONAL T.V.
For TV
For True Shape

Types of Section Planes
1. Section Plane Perpendicular to HP and
parallel to VP.
2. Section Plane Perpendicular to VP and
parallel to HP.
3. Section Plane Perpendicular to VP and
Inclined to HP.
4. Section Plane Perpendicular to HP and
Inclined to VP.
5. Section Plane Perpendicular to both HP and
VP.

Problem 1
A rectangular prism, side of base 40 mm X 25
mm and height 60 mm, rests with its base on
HP such that one of its larger rectangular
faces is parallel to VP. A section plane
perpendicular to HP and parallel to VP cuts
the prism into two equal halves. Draw its top
view and sectional front view.

Ravi Sivaprakash AP/MECH AAMEC
Kovilvenni

V.P
.
X Y
H.P
.
Problem 1
25
60
40

Problem 2
A cube of side 25 mm rests on the HP on one
of its faces with a vertical face inclined at 35°
to the VP. A plane perpendicular to the HP
and parallel to the VP cuts the cube 10 mm
away from the axis and farther away from
the VP. Draw the top view and the sectional
front view.

V.P
.
X Y
H.P
.
Problem 2 Draw the top view as a square of side 40 mm
with one of its sides inclined at 35° to xy.
35°
t (p)
2
u(q)
w (s)
25
t’
p’
(w’) u’
(s’)
v’
25
o
4’ 3’ r’
1
10
1’ 2’
v (r)
q’
(4) (3)

Problem 3
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 the HP meeting
the axis at 25 mm above the base. Draw its
front view, sectional top view and the true
shape of the section.

V.P
.
X Y
H.P
.
Problem 3
Faces equally inclined to the VP.
45°
p (t)
2
q(u)
s (w)
p’
t’
q’(s’)
u’(w’)
r’
30
3’
v’
1
1’
2’
r (v)
45°
25
30°
3
4
5
Draw another reference line X1Y1
parallel to the section plane.
X1
y1
Draw projectors perpendicular
to X1Y1 from 1’, 2’, 3’, (4’), (5’)
11
The distance of 11 from X1Y1 = t’-1
The distance of 21 from X1Y1 = u’-2
The distance of 31 from X1Y1 = XY -3
21 31
41
51
True shape
of section
Sectional top
view
Removed
Portion
Section plane
(5’)
(4’)

Problem 4
A cube of side 40 mm is placed and cut by a
plane in such a way that the true shape of
the section is a regular hexagon. Draw the
front and top views of the cube and
determine the inclination of the plane with
the HP.

V.P
.
X Y
H.P
.
Problem 4
The mid-points of p’q’ are marked as 1’
The mid-points of q’u’ are marked as 2’
The mid-points of u’v’ are marked as 3’
45°
p (t)
2
q(u)
s (w)
p’
t’
q’(s’)
u’(w’)
r’
40
3’
v’
1
1’
2’
r (v)
45°
3
4
5
X1
y1
to X1Y1 from 1’, 2’, 3’, (4’), (5’)
True shape
of section
6
11
21
31
41
51
61
(6’)
(5’)
(4’)

Problem 5
A square prism of base side 30 mm and height
60 mm rests on the HP on one of its ends
with two of its rectangular faces equally
inclined to the VP. It is cut by a plane
perpendicular to the VP and inclined at 60°
to the HP meeting the axis at 15 mm from
the top. Draw its front view, sectional top
view and the true shape of the section.

V.P
.
X Y
H.P
.
Problem 5
Faces equally inclined to the VP.
45°
p (t)
2
q(u)
s (w)
p’
t’
q’(s’)
u’(w’)
r’
60
3’
v’
1
1’
2’
r (v)
45°
15
60°
3
4
5
Draw another reference line X1Y1
parallel to the section plane.
X1
y1
to X1Y1 from 1’, 2’, 3’, (4’), (5’)
11
21 31
41
51
True shape
of section
Sectional top
view
30
(5’)
(4’)

Problem 6
A square prism of height 80 mm and base of
diagonal 40 mm rests on the HP on its base
with base edges equally inclined to the VP. It
is cut by a section plane passing through the
mid-point of the axis of the prism
perpendicular to the VP and inclined to the
HP. Find the inclination of the cutting plane if
the true shape of the section is a rhombus of
diagonals 60 mm and 40 mm.

V.P
.
X Y
H.P
.
Problem 6
Draw the top and front views of
the prism with its base edges
equally inclined to the VP.
pr=qs=40 mm.
p (t)
2
s(w)
q (u)
p’
t’
s’(q’)
w’(u’)
r’
80
3’
v’
1
1’
2’(4’)
r (v)
40
48°
3
4
X1
y1
11
21
31
41
Locate the mid-point of the axis
in the front view.
With 2’ as centre and half of the
longer diagonal of the rhombus
forming the true shape (30 mm)
as radius, draw arcs cutting the
extreme vertical edges at 1’ and
3’.

Problem 7
A hollow square prism of base side 50 mm
(outside), thickness 10 mm and axis length 70
mm is resting on the HP on one of its ends
with a vertical face making 45° with the VP. It
is cut by a plane perpendicular to the VP and
inclined at 30° to the HP. The cutting plane
meets the axis at 17 mm from the top. Draw
the front view, sectional top view and true
shape of the section. Page no 258

Problem 8
A hexagonal prism of base side 30 mm and axis
length 70 mm rests on one of its ends on the
HP with two base sides parallel to the VP. It is
cut by a plane perpendicular to the VP and
inclined at 30° to the HP. The cutting plane
meets the axis at 30 mm from the top. Draw
the front view, sectional top view and the
true shape of the section.

Problem 8
V.P
.
X Y
H.P
.
1’
4’
3’
2’
70
1
2 3
4
5
30°
X1
y1
30
11
6
30
21
31
41
51
61
(5’)
(6’)
Kovilvenni

Problem 9
A hexagonal prism of base side 40 mm and
height 100 mm rests on the HP on one of its
ends with two rectangular faces parallel to
the VP. It is cut by a plane perpendicular to
the VP and inclined at 45° to the HP. The
cutting plane meets the axis at 30 mm from
the top. Draw the front view, sectional top
view and the true shape of the section.page
no 253
Kovilvenni

Problem 10
A pentagonal prism of base side 30 mm and
length 70 mm is lying on the HP on one of its
rectangular faces with its axis perpendicular
to the VP. It is cut by a plane perpendicular
to the VP and inclined at 45° to the HP. The
shortest distance between the axis and the
cutting plane is 10 mm. Draw the front view,
sectional top view and the true shape of the
section. Page no 251
Kovilvenni

Problem 10

Problem 11
A pentagonal prism of base side 30 mm and axis
length 75 mm rests on the HP on one of its
ends with a rectangular face parallel to the
VP. It is cut by a plane perpendicular to the
VP and inclined at 30° to the HP and meeting
the axis at 25 mm from the top. Draw the
front view, sectional top view and the true
shape of the section. Page no 290
Kovilvenni

Problem 12
A Square pyramid of base side 25 mm and
altitude 40 mm rests on the HP on its base
with the base edges equally inclined to the
VP. It is cut by a plane perpendicular to the
VP and inclined at 30° to the HP meeting the
axis at 21 mm above the HP. Draw the
section.
Kovilvenni

V.P
.
X Y
H.P
.
Problem 12 Faces equally inclined to the VP.
45°
p
2
q
s
p’ q’(s’)
40
3’
r’
1
1’
2’(4’)
r
45°
21
30°
3
4
Points 2’ and 4’ cannot be
projected directly. For this draw
a line through 2’ parallel to the
base to meet o’p’.
X1
y1
11
The distance of 11 from X1Y1 = XY-1
21
31
41
True shape
of section
Sectional top
view
25
o
o’
a’
a
With o as centre and “oa” as
radius, draw arc to meet oq at 2
and os at 4.
Kovilvenni

Problem 13
A Square pyramid of base side 30 mm and axis
60 mm long is standing on HP with its base
edges equally inclined to VP. It is cut by a
section plane perpendicular to VP and
inclined at 30° to HP, bisecting the axis. Draw
the sectional top view and the true shape of
the section, if the upper portion is removed.
Page no 14.15
Kovilvenni

Problem 14
A square pyramid of base side 40 mm and axis
65 mm rests on its base on HP. A cutting
plane inclined to HP and perpendicular to VP
cuts the pyramid in such a way that the true
shape of the section is a trapezium of parallel
sides measuring 30 mm and 20 mm. Draw its
section. Also find the inclination of the
cutting plane to the HP. Page no 267
Kovilvenni

Problem 14
Kovilvenni

Problem 15
A hexagonal pyramid of base side 25 mm and
axis 55 mm rests on its base on the HP with
two base edges perpendicular to the VP. It is
cut by a plane perpendicular to the VP and
inclined at 30° to the HP meeting the axis at
20 mm from the vertex. Draw the front view,
section.
Kovilvenni

V.P
.
X Y
H.P
.
Problem 15
p 2
q
s
p’(u’) q’(t’)
55
3’(4’)
r’(s’)
1
1’(6’)
2’(5’)
r
20
30°
3
5
Points 2’ and 5’ cannot be
projected directly. For this draw
a line through 2’ parallel to the
base to meet o’p’.
X1
y1
11
21
31
41
True shape
of section
Sectional top
view
25
o
o’
a’
a
With o as centre and “oa” as
radius, draw arc to meet oq at 2
and os at 5.
t
u
4
6
51
61
Kovilvenni

Problem 16
A hexagonal pyramid of base side 20 mm and
altitude 50 mm rests on its base on the HP
with two edges of the base perpendicular to
the VP. A cutting plane parallel to the HP cuts
the pyramid at a height of 20 mm above the
base. Draw the front view and the sectional
top view. Page no 259
Kovilvenni

Problem 16
Kovilvenni

Problem 17
A hexagonal pyramid side of base 30 mm and
height 65 mm is resting on its base on HP
with two edges parallel to VP. Its is cut by a
plane perpendicular to VP, inclined at 45° to
HP and intersecting the axis at a point 25 mm
above the base. Draw the sectional top view
and true shape of section. Page no 14.13
Kovilvenni

Problem 18
A pentagonal pyramid of base side 20 mm and
altitude 55 mm rests on its base on the HP
with one of the base edges perpendicular to
the VP. It is cut by a plane inclined at 50° to
the base. The cutting plane meets the axis at
15 mm above the base. Draw the front view,
section.
Kovilvenni

Problem 18
V.P
.
X Y
H.P
.
20
p
t
s
r
q
o
o’
55
p’(t’) r’
q’(s’)
50°
11
15
1’
2’
3’
(4’)
(5’)
(6’)
X1
y1
21
31
41
51
61
1
2
3
4
5
6
Kovilvenni

Problem 18A
A Pentagonal pyramid of base side 40 mm and
height 80 mm rests on the base such that
one base edge is perpendicular to VP. It is cut
by a section plane inclined at 45° to HP and
passing through the mid-point of the axis
removing the apex. Draw the front view,
sectional top view and true shape of the
section. (Univ Qstn)
Kovilvenni

Problem 19
A cylinder of diameter 40 mm and height 50 mm
rests on its base on the HP. It is cut by a
plane perpendicular to the VP and inclined at
50° to the HP. The cutting plane meets the
axis at a distance of 15 mm from the top.
Draw the front view, sectional top view and
the true shape of the section.
Kovilvenni

Problem 19
V.P
.
X Y
H.P
.
50
p’ q’ r’ s’ t’
a’
e’
50°
p(a)
q(b)
r(c)
s(d)
t(e)
(u’)
(v’)
(w’)
d’(f’)
c’(g’)
b’(h’)
u(f)
w(h)
v(g)
11
φ40
15
X1
y1
1’
2’(7’)
3’(6’)
4’(5’)
1
2
3
4
5
6
7
21
31
41
51
61
71
Kovilvenni

Problem 20
is having its axis vertical. It is cut by a plane
perpendicular to VP and inclined at 30° to
HP. The plane bisects the axis of the cylinder.
Draw its front view, sectional top view,
sectional side view and true shape of section.
Page no 14.20
Kovilvenni

Problem 21
has a central hexagonal slot of side 20 mm
running right through the length. The
cylinder is lying on the HP with its axis
perpendicular to the VP. A vertical cutting
plane cuts the cylinder in such a way that it
meets the bases at 6 mm from diametrically
opposite ends. Draw the sectional front view
and the true shape of the section.
Kovilvenni

Problem 21
V.P
.
X Y
H.P
.
80
1’ 2’
3’
4’
1’1
2’1
First consider cylinder and
name the section points as
1’,2’,3’,4’
3’1
4’1 5’1
φ60
Then consider hexagonal
slot separately. Name the
section points as
5’,6’,7’,8’,9’,10’
1
2(3)
(4)
6
20
(5)
(6)
(7)
(8)
(9)
(10)
5’
6’
7’
9’
8’
10’
X1
y1
6’1
7’1
8’1
9’1
10’1
Kovilvenni

Problem 22
A cone base 50 mm diameter and axis 65 mm
long, rests with its base on the HP. It is cut by
a section plane perpendicular to VP, inclined
at 45° to HP and passing through a point on
the axis 35 mm above the base. Draw the
section.
Kovilvenni

Problem 22
V.P
.
X Y
H.P
.
65
o’
p’ t’
45°
p
q
r
s
t
s’(u’)
r’(v’)
q’(w’)
u
w
v
11
φ50
35
X1
y1
1’
2’(8’)
3’(7’)
4’(6’)
1
2 3
4
5
6
7
21
31
41
51
61
71
o
5’
8
a’
a
81
Kovilvenni

Problem 23
A cone of base diameter 40 mm and height 50
mm rests on its base on the HP. It is cut by a
plane perpendicular to the VP and inclined
at 40° to HP. The cutting plane meets the axis
at 20 mm from the vertex. Draw the
section. Page no 280
Kovilvenni

Problem 23
Kovilvenni

Problem 24
A cone, base 40 mm diameter and axis 60 mm
long, rests with its base on HP. It is cut by a
section plane perpendicular to VP, parallel to
one of the end generators and passing
through a point on the axis 25 mm from the
apex. Draw the sectional top view and the
Kovilvenni

Problem 24
V.P
.
X Y
H.P
.
60
o’
p’ t’
p
q
r
s
t
s’(u’)
r’(v’)
q’(w’)
u
w
v
11
φ40
25
X1
y1
1’(7’)
2’(6’)
3’(5’)
4’
1
2
3
5
6
7
21
31
41
51
61
71
o 4
a’
a
Kovilvenni

Problem 25
A cone of base diameter 50 mm and altitude 60
plane perpendicular to the VP and parallel to
one of the extreme generators, 10 mm away
from it. Draw the sectional top view and the
true shape of the section. Page no 282
Kovilvenni

Problem 25
Kovilvenni

Problem 26
A cone of base diameter 40 mm and altitude 50
section plane perpendicular to the VP and
inclined at 80° to the HP, passing through the
apex. Draw the sectional top view and the
true shape of the section. Page no 285
Kovilvenni

Problem 27
A hexagonal prism of base side 30 mm and axis
length 70 mm rests on the HP on one of its
rectangular faces with its axis perpendicular
to the VP. It is cut by a vertical plane inclined
at 30° to the VP. The cutting plane meets the
axis at a distance of 30 mm from one end.
Draw the top view, sectional front view and
the true shape of the section.
Kovilvenni

Problem 27
V.P
.
X Y
H.P
.
30
2’ 3’
4’
5’
6’
1’
70
p q r s
(t)
(u)
e h
g(i)
f(j)
30°
30
X1
y1
1
2(6)
3(5)
4
61’ 21’= 6’ 2’
51’ 31’= 5’ 3’
21’
51’
61’
31’
11’
41’
30°
Kovilvenni

Problem 28
A cube of side 25 mm rests on the HP on one
of its faces with a vertical face inclined at 35°
to the VP. A plane perpendicular to the HP
and inclined at 50° to the VP cuts the cube, 3
mm away from the axis. Draw the top view
and the sectional front view. Also draw the
Kovilvenni

V.P
.
X Y
H.P
.
Problem 28
35°
t (p)
2(3)
u(q)
w (s)
25
t’
p’
(w’) u’
(s’)
v’
25
o
4’ 3’ r’
1 (4)
3
1’ 2’
v (r)
q’
50°
50°
X1
y1
4”
1” 4”= 1’ 4’
2” 3”= 2’ 3’
3”
1”
2”
Section(apparent)
Removed
True
shape of
section
Section plane
Auxiliary
plane
parallel to
section
plane
Sectional front
view
Kovilvenni

sections of solids engineering graphics unit iv

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