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SECTIONS OF SOLIDS
 Some times the objects are so complicated that, it becomes very difficu
lt to visualize the object with the help of its front view and top view.
 Some objects are hollow. Their internal details are not visible with the
help of simple front view and top view.
 In such cases the object is cut by some imaginary cutting plane to und
erstand internal details of that object.
First let us know the types of cutting planes.
The action of cutting is called SECTIONING a solid
&
The plane of cutting is called SECTION PLANE.
θº
غ
A.V.P.
 to HP &  to VP
PLANES
PRINCIPAL PLANES
HP AND VP
AUXILIARY PLANES
Auxiliary Vertical Plane
(A.V.P.)
Profile Plane
( P.P.)
Auxiliary Inclined Plane
(A.I.P.)
1
An A.V.P. appears as a straight line in its top view. The st
raight line is its H.T.
So an A.V.P. always cuts T.V. of a solid, Its position is de
scribed in the problem.
X Y
As per B.I.S. the cutting
plane is shown as centre li
ne inside the object and a
s solid line out side the obj
ect
Remember:-
1. After launching a section plane eit
her in FV or TV, the part towards
observer is assumed to be remove
d.
2. As far as possible the smaller part
is assumed to be removed.
H
T
Properties of section lines:
1. They are light.
2. Inclined at 45º with the reference li
ne.
3. 1 to 2 mm apart.
observer
An A.I.P. appears as a straight line in its front view. The straight li
ne is its V.T. So an A.I.P. always cuts F.V. of a solid. Its position is
described in the problem
X Y
V
T
As per B.I.S. the cutting p
lane is shown as centre lin
e inside the object and as
solid line out side the obje
ct
Remember:-
1. After launching a section plane e
ither in FV or TV, the part toward
s observer is assumed to be remo
ved.
2. As far as possible the smaller par
t is assumed to be removed.
observer
Properties of section lines:
1. They are light.
2. Inclined at 45º with the refer
ence line.
3. 1 to 2 mm apart.
SECTIONING A SOLID
An object ( here a solid ) is cut by some imag
inary cutting plane to understand internal d
etails of that object.
The action of cutting is called
SECTIONING a solid
&
The plane of cutting is called
SECTION PLANE.
Two cutting actions means section planes are recommended.
A) Section Plane perpendicular to VP and inclined to HP.
( This is a definition of an Aux. Inclined Plane i.e. A.I.P.)
NOTE:- This section plane appears as a straight line in FV.
B) Section Plane perpendicular to HP and inclined to VP.
( This is a definition of an Aux. Vertical Plane i.e. A.V.P.
)
NOTE:- This section plane appears as a straight line in TV.
Remember:-
1. After launching a section plane either in FV or TV, t
he
part towards observer is assumed to be removed.
2. As far as possible the smaller part is assumed to be r
emoved.
OBSERVER
ASSUME
UPPER PART
REMOVED
OBSERVER
ASSUME
LOWER PART
REMOVED
(A)
(B)
ILLUSTRATION SHOWING
IMPORTANT TERMS
IN SECTIONING.
x y
TRUE SHAPE
Of SECTION
SECTION
PLANE
SECTION LINES
(450 to XY)
Apparent Shape
of section
SECTIONAL T.V.
For TV
Section Plane
Through Apex
Section Plane
Through Generators
Section Plane Parallel
to end generator.
Section Plane
Parallel to Axis.
Triangle Ellipse
Hyperbola
Ellipse
Cylinder through
generators.
Sq. Pyramid through
all slant edges
Trapezium
Typical Section Planes
&
Typical Shapes
Of
Sections.
• The surface created by cutting the object by a section plane is called as section.
• The section is indicated by drawing the hatching lines (section lines) within the sectioned area.
• The hatching lines are drawn at 45° to the principal outlines or the lines of symmetry of the section
• The spacing between hatching lines should be uniform and in proportion to the size of the section.
Hatching of the Sections
H or
HB
2H
SECTIONAL VIEW – PARALLEL TO H.P AND PERPENDICUL
AR TO V.P
A cube of 40 mm sideis cut by a horizontal section plane, parallel t
o H.P at a distance of 15 mm from the top end. Draw the sectional
top view and front view
Problem: A square pyramid, base 40 mm side and axis 65 mm long, has its base on the HP with t
wo edges of the base perpendicular to the VP. It is cut by a section plane, perpendicular to the VP
, inclined at 45º to the HP and bisecting the axis. Draw its sectional top view, sectional side view
and true shape of the section.
X
o’
Y
a b
c
d
o
a’ d’ b’ c’
1
2
3
4
1’ 4’
2’ 3’
2
3
1
4
Sectional T
op View
True shape of
the section
a” b” d” c”
o”
1” 4”
2” 3”
Sectional s
ide View
Properties of section lines:
1. They are light.
2. Inclined at 45º with the
reference line.
3. 1 to 2 mm apart.
Problem: A square pyramid, base 40 mm side and axis 65 mm long, has its base on the HP and a
ll the edges of the base equally inclined to the VP. It is cut by a section plane, perpendicular to th
e VP, inclined at 45º to the HP and bisecting the axis. Draw its sectional top view, sectional side
view and true shape of the section.
X Y
45º
a
b
c
d
o
a’
b’
c’
d’
o’
1
2
3
4
1’
2’
3’
4’
11
41
21 31
X1
Y1
d” a” c” b”
o”
3”
2”
4”
1”
True shape
of the secti
on
Sectional si
de View
Problem: A pentagonal pyramid , base 30mm side and axis 60 mm long is lying on one of its triangular faces
on the HP with the axis parallel to the VP. A vertical section plane, whose HT bisects the top view of the axis
and makes an angle of 30º with the reference line, cuts the pyramid removing its top part. Draw the top view,
sectional front view and true shape of the section and development of the surface of the remaining portion of
the pyramid.
X Y
a
b
c
d
e
o
a’ b’e’
c’d’
o’
60
30
c’d’ o’
a’
b’e’
a1
b1
c1
d1
e1
o1
1’
2’
3’
4’
5’
6’
1
2
3
4
5
6 31’
41’
21’
11’
61’
51’
a
b c
d
e
f
a’ b’f’ c’e’ d’
o
o’
1
2
3
4
5
6
7
1’7’
2’6’
3’5’
4’
Problem: A hexagonal pyramid, base 30 mm side and axis 65 mm long is resting on its base on
the HP, with two edges of the base parallel to the VP. It is cut by a section plane perpendicular t
o VP and inclined at 45º to the HP, intersecting the axis at a point 25 mm above the base. Draw
the front view, sectional top view, sectional side view and true shape of the section.
25
65
X1
Y1
11
71
21
61
31
51
41
X2
Y2
b”
c”
a”
d”
f”
e”
o”
1” 7”
2” 6”
3” 5”
4”
Problem: A square prism base 40 mm side, axis 80 mm long, has its base on the H.P. and its fa
ces equally inclined to the V.P. It is cut by a plane, perpendicular to the V.P., inclined at 60º to t
he H.P. and passing through a point on the axis, 55 mm above the H.P. Draw its front view, sect
ional top view and another top view on an A.I.P. parallel to the section plane.
X Y
a,1
45º
a’
b’
d’ c’
b,2
c,3
d,4
1’
2’
4’ 3’
55
30º
p
q
r
s
t
p’
q’
r’
s’
t’
x1
y1
a1
11
c1
31
d1
41
b1
21
t1
p1
s1
q1
r1
Problem: A Hexagonal prism has a face on the H.P. and the axis parallel to the V.P. It is cut by a vertical s
ection plane the H.T. of which makes an angle of 45 with XY and which cuts the axis at a point 20 mm fro
m one of its ends. Draw its sectional front view and the true shape of the section. Side of base 25 mm long h
eight 65mm.
X Y
a
b
c
d
e
f
a’ b’ c’
d’
e’
f’
25
65
a’ b’ c’
d’
e’
f’
a’
b’
c’d’
e’
f’
a’
b’
c’d’
e’
f’
d1
a1
b1
c1
e1
f1
d1
a1
b1
c1
e1
f1
20
1’
2’
3’
4’
5’
6’ 7’
1 2
3
4
5
6
7
X1
Y1
31’
41’
21’
11’
71’
61’
51’
Problem: A cylinder of 40 mm diameter, 60 mm height and having its axis vertical, is cut by a se
ction plane perpendicular to the V.P., inclined at 45º to the H.P. and intersecting the axis 32 mm a
bove the base. Draw its front view, sectional top view, sectional side view and true shape of the s
ection.
X Y
Ø 40
60
32
45º
1
2
3
4
5
6
7
8
9
10
11
12
1’ 2’ 3’
4’
5’
6’
7’
8’
9’
10’
11’ 12’
x1
y1
1” 2” 3” 4” 5’ 6” 7”
8”
9”
10”
11”
12”
p”4
p”3 p”5
p”2 p”6
p”1 p”7
p”12 p”8
p”11
p”9
p”10
p10
p4
x2
y2
p11
p3
p12
p2
p1
p9
p5
p6
p8
p7
X Y
1
2
3
4
5
6
7
8
9
10
11
12
Problem: A Cone base 75 mm diameter and axis 80 mm long is resting on its base on H.P. It is cut by a secti
on plane perpendicular to the V.P., inclined at 45º to the H.P. and cutting the axis at a point 35 mm from the a
pex. Draw the front view, sectional top view, sectional side view and true shape of the section.
1’
2’
12’
3’
11’
4’
10’
5’
9’
6’
8’ 7’
o
o’
35
a
b
k
c
d
l
e
f
g
h
i
j
a’
b’
k’
c’
d’
l’
e’
f’
g’
h’
i’
j’
X1
Y1
4” 5” 6” 7” 8” 9”10”
11”
12”
1”
2”
3”
o”
a”
b”
c”
d”
e”
f”
g”
h”
i”
j”
k”
l”
Problem: A cone, base 75 mm diameter and axis 80 mm long is resting on its base on the HP. It i
s cut by a section plane perpendicular to the VP, and parallel to and 12 mm away from one of its
generators. Draw the front view, sectional top view and true shape of the section. Draw the front
view, sectional top view and sectional side view.
x y
Ø75
1
2
3
4
5
6
7
8
9
10
11
12
80
10’ 11’
9’
12’
8’
9’7’ 2’
6’
3’
5’
4’
O
O’
X1
Y1
X2
Y2
1” 12”
2”
11”
3”
10” 9”
5”
8”
6”
7”
4”
O”
X Y
1
2
3
4
5
6
7
8
9
10
11
12
Problem: A cylinder 55 mm diameter and 65 mm long, has its axis parallel to both the HP and the VP. It is c
ut by a vertical section plane inclined at 30º to the VP so that axis is cut at a point 25 mm from one of its ends
and both the bases of cylinder are partly cut. Draw its sectional front view and true shape of the section.
1’
2’
12’
3’ 1
1’
4’ 1
0’
5’
9’
6’
8’ 7’
1’
2’ 12’
3’ 11’
4’ 10’
5’ 9’
6’ 8’
7’
4
3,5
2,6
1,7
8,12
9,11
10
25
p2’
p6’
p1’
p7’
p12’
p8’
Problem: : A square prism axis 110 mm long is resting on its base in the H.P. the edges of the ba
se are equally inclined to the V.P. The prism is cut by an A.I.P. passing through the mid point of t
he axis in such a way that the true shape of the section is a rhombus having diagonals of 100 mm
and 50 mm. Draw the projections and determine the inclination of A.I.P. with the H.P.
Here we are not given side of base of square prism. But the shorter diagonal of the rhombus will be equal to base diagonal of
the prism. So to begin with, draw a square in the top view with base diagonal 50 mm.
X Y
50 a
b
c
d
110
The inclination of the cutting plane decides the length of longer diagonal. From the mid point of the axis cut two arcs of 50 m
m radius, one on long edge ‘b’ and the other on the long edge ‘d’
X1
Y1
11
21
41
31
1
1’
2’ 4’
3’
2
3
4
Problem: A cone, diameter of the base 60 mm and axis 70 mm long is resting on its base on the
H.P. It is cut by an A.I.P. so that the true shape of the section is an isosceles triangle having 50 m
m base. Draw the plan, the elevation and the true shape of the section.
X Y
70
60
25
25
o’
o
a
b
a’ b’
o1
a1
b1
6
45
55
Problem: A cone, base 45 mm diameter and axis 55 mm long is resting on the H.P. on its base. It
is cut by a section plane, perpendicular to both the H.P. and the V.P. and 6 mm away from the axi
s. Draw its front view, top view and sectional side view.

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Engineering Drawing section of solid

  • 2.  Some times the objects are so complicated that, it becomes very difficu lt to visualize the object with the help of its front view and top view.  Some objects are hollow. Their internal details are not visible with the help of simple front view and top view.  In such cases the object is cut by some imaginary cutting plane to und erstand internal details of that object. First let us know the types of cutting planes. The action of cutting is called SECTIONING a solid & The plane of cutting is called SECTION PLANE.
  • 3. θº Øº A.V.P.  to HP &  to VP PLANES PRINCIPAL PLANES HP AND VP AUXILIARY PLANES Auxiliary Vertical Plane (A.V.P.) Profile Plane ( P.P.) Auxiliary Inclined Plane (A.I.P.) 1
  • 4. An A.V.P. appears as a straight line in its top view. The st raight line is its H.T. So an A.V.P. always cuts T.V. of a solid, Its position is de scribed in the problem. X Y As per B.I.S. the cutting plane is shown as centre li ne inside the object and a s solid line out side the obj ect Remember:- 1. After launching a section plane eit her in FV or TV, the part towards observer is assumed to be remove d. 2. As far as possible the smaller part is assumed to be removed. H T Properties of section lines: 1. They are light. 2. Inclined at 45º with the reference li ne. 3. 1 to 2 mm apart. observer
  • 5. An A.I.P. appears as a straight line in its front view. The straight li ne is its V.T. So an A.I.P. always cuts F.V. of a solid. Its position is described in the problem X Y V T As per B.I.S. the cutting p lane is shown as centre lin e inside the object and as solid line out side the obje ct Remember:- 1. After launching a section plane e ither in FV or TV, the part toward s observer is assumed to be remo ved. 2. As far as possible the smaller par t is assumed to be removed. observer Properties of section lines: 1. They are light. 2. Inclined at 45º with the refer ence line. 3. 1 to 2 mm apart.
  • 6. SECTIONING A SOLID An object ( here a solid ) is cut by some imag inary cutting plane to understand internal d etails of that object. The action of cutting is called SECTIONING a solid & The plane of cutting is called SECTION PLANE. Two cutting actions means section planes are recommended. A) Section Plane perpendicular to VP and inclined to HP. ( This is a definition of an Aux. Inclined Plane i.e. A.I.P.) NOTE:- This section plane appears as a straight line in FV. B) Section Plane perpendicular to HP and inclined to VP. ( This is a definition of an Aux. Vertical Plane i.e. A.V.P. ) NOTE:- This section plane appears as a straight line in TV. Remember:- 1. After launching a section plane either in FV or TV, t he part towards observer is assumed to be removed. 2. As far as possible the smaller part is assumed to be r emoved. OBSERVER ASSUME UPPER PART REMOVED OBSERVER ASSUME LOWER PART REMOVED (A) (B)
  • 7. ILLUSTRATION SHOWING IMPORTANT TERMS IN SECTIONING. x y TRUE SHAPE Of SECTION SECTION PLANE SECTION LINES (450 to XY) Apparent Shape of section SECTIONAL T.V. For TV
  • 8. Section Plane Through Apex Section Plane Through Generators Section Plane Parallel to end generator. Section Plane Parallel to Axis. Triangle Ellipse Hyperbola Ellipse Cylinder through generators. Sq. Pyramid through all slant edges Trapezium Typical Section Planes & Typical Shapes Of Sections.
  • 9.
  • 10.
  • 11.
  • 12. • The surface created by cutting the object by a section plane is called as section. • The section is indicated by drawing the hatching lines (section lines) within the sectioned area. • The hatching lines are drawn at 45° to the principal outlines or the lines of symmetry of the section • The spacing between hatching lines should be uniform and in proportion to the size of the section. Hatching of the Sections H or HB 2H
  • 13.
  • 14.
  • 15.
  • 16. SECTIONAL VIEW – PARALLEL TO H.P AND PERPENDICUL AR TO V.P A cube of 40 mm sideis cut by a horizontal section plane, parallel t o H.P at a distance of 15 mm from the top end. Draw the sectional top view and front view
  • 17. Problem: A square pyramid, base 40 mm side and axis 65 mm long, has its base on the HP with t wo edges of the base perpendicular to the VP. It is cut by a section plane, perpendicular to the VP , inclined at 45º to the HP and bisecting the axis. Draw its sectional top view, sectional side view and true shape of the section. X o’ Y a b c d o a’ d’ b’ c’ 1 2 3 4 1’ 4’ 2’ 3’ 2 3 1 4 Sectional T op View True shape of the section a” b” d” c” o” 1” 4” 2” 3” Sectional s ide View Properties of section lines: 1. They are light. 2. Inclined at 45º with the reference line. 3. 1 to 2 mm apart.
  • 18. Problem: A square pyramid, base 40 mm side and axis 65 mm long, has its base on the HP and a ll the edges of the base equally inclined to the VP. It is cut by a section plane, perpendicular to th e VP, inclined at 45º to the HP and bisecting the axis. Draw its sectional top view, sectional side view and true shape of the section. X Y 45º a b c d o a’ b’ c’ d’ o’ 1 2 3 4 1’ 2’ 3’ 4’ 11 41 21 31 X1 Y1 d” a” c” b” o” 3” 2” 4” 1” True shape of the secti on Sectional si de View
  • 19. Problem: A pentagonal pyramid , base 30mm side and axis 60 mm long is lying on one of its triangular faces on the HP with the axis parallel to the VP. A vertical section plane, whose HT bisects the top view of the axis and makes an angle of 30º with the reference line, cuts the pyramid removing its top part. Draw the top view, sectional front view and true shape of the section and development of the surface of the remaining portion of the pyramid. X Y a b c d e o a’ b’e’ c’d’ o’ 60 30 c’d’ o’ a’ b’e’ a1 b1 c1 d1 e1 o1 1’ 2’ 3’ 4’ 5’ 6’ 1 2 3 4 5 6 31’ 41’ 21’ 11’ 61’ 51’
  • 20. a b c d e f a’ b’f’ c’e’ d’ o o’ 1 2 3 4 5 6 7 1’7’ 2’6’ 3’5’ 4’ Problem: A hexagonal pyramid, base 30 mm side and axis 65 mm long is resting on its base on the HP, with two edges of the base parallel to the VP. It is cut by a section plane perpendicular t o VP and inclined at 45º to the HP, intersecting the axis at a point 25 mm above the base. Draw the front view, sectional top view, sectional side view and true shape of the section. 25 65 X1 Y1 11 71 21 61 31 51 41 X2 Y2 b” c” a” d” f” e” o” 1” 7” 2” 6” 3” 5” 4”
  • 21. Problem: A square prism base 40 mm side, axis 80 mm long, has its base on the H.P. and its fa ces equally inclined to the V.P. It is cut by a plane, perpendicular to the V.P., inclined at 60º to t he H.P. and passing through a point on the axis, 55 mm above the H.P. Draw its front view, sect ional top view and another top view on an A.I.P. parallel to the section plane. X Y a,1 45º a’ b’ d’ c’ b,2 c,3 d,4 1’ 2’ 4’ 3’ 55 30º p q r s t p’ q’ r’ s’ t’ x1 y1 a1 11 c1 31 d1 41 b1 21 t1 p1 s1 q1 r1
  • 22. Problem: A Hexagonal prism has a face on the H.P. and the axis parallel to the V.P. It is cut by a vertical s ection plane the H.T. of which makes an angle of 45 with XY and which cuts the axis at a point 20 mm fro m one of its ends. Draw its sectional front view and the true shape of the section. Side of base 25 mm long h eight 65mm. X Y a b c d e f a’ b’ c’ d’ e’ f’ 25 65 a’ b’ c’ d’ e’ f’ a’ b’ c’d’ e’ f’ a’ b’ c’d’ e’ f’ d1 a1 b1 c1 e1 f1 d1 a1 b1 c1 e1 f1 20 1’ 2’ 3’ 4’ 5’ 6’ 7’ 1 2 3 4 5 6 7 X1 Y1 31’ 41’ 21’ 11’ 71’ 61’ 51’
  • 23. Problem: A cylinder of 40 mm diameter, 60 mm height and having its axis vertical, is cut by a se ction plane perpendicular to the V.P., inclined at 45º to the H.P. and intersecting the axis 32 mm a bove the base. Draw its front view, sectional top view, sectional side view and true shape of the s ection. X Y Ø 40 60 32 45º 1 2 3 4 5 6 7 8 9 10 11 12 1’ 2’ 3’ 4’ 5’ 6’ 7’ 8’ 9’ 10’ 11’ 12’ x1 y1 1” 2” 3” 4” 5’ 6” 7” 8” 9” 10” 11” 12” p”4 p”3 p”5 p”2 p”6 p”1 p”7 p”12 p”8 p”11 p”9 p”10 p10 p4 x2 y2 p11 p3 p12 p2 p1 p9 p5 p6 p8 p7
  • 24.
  • 25. X Y 1 2 3 4 5 6 7 8 9 10 11 12 Problem: A Cone base 75 mm diameter and axis 80 mm long is resting on its base on H.P. It is cut by a secti on plane perpendicular to the V.P., inclined at 45º to the H.P. and cutting the axis at a point 35 mm from the a pex. Draw the front view, sectional top view, sectional side view and true shape of the section. 1’ 2’ 12’ 3’ 11’ 4’ 10’ 5’ 9’ 6’ 8’ 7’ o o’ 35 a b k c d l e f g h i j a’ b’ k’ c’ d’ l’ e’ f’ g’ h’ i’ j’ X1 Y1 4” 5” 6” 7” 8” 9”10” 11” 12” 1” 2” 3” o” a” b” c” d” e” f” g” h” i” j” k” l”
  • 26. Problem: A cone, base 75 mm diameter and axis 80 mm long is resting on its base on the HP. It i s cut by a section plane perpendicular to the VP, and parallel to and 12 mm away from one of its generators. Draw the front view, sectional top view and true shape of the section. Draw the front view, sectional top view and sectional side view. x y Ø75 1 2 3 4 5 6 7 8 9 10 11 12 80 10’ 11’ 9’ 12’ 8’ 9’7’ 2’ 6’ 3’ 5’ 4’ O O’ X1 Y1 X2 Y2 1” 12” 2” 11” 3” 10” 9” 5” 8” 6” 7” 4” O”
  • 27. X Y 1 2 3 4 5 6 7 8 9 10 11 12 Problem: A cylinder 55 mm diameter and 65 mm long, has its axis parallel to both the HP and the VP. It is c ut by a vertical section plane inclined at 30º to the VP so that axis is cut at a point 25 mm from one of its ends and both the bases of cylinder are partly cut. Draw its sectional front view and true shape of the section. 1’ 2’ 12’ 3’ 1 1’ 4’ 1 0’ 5’ 9’ 6’ 8’ 7’ 1’ 2’ 12’ 3’ 11’ 4’ 10’ 5’ 9’ 6’ 8’ 7’ 4 3,5 2,6 1,7 8,12 9,11 10 25 p2’ p6’ p1’ p7’ p12’ p8’
  • 28. Problem: : A square prism axis 110 mm long is resting on its base in the H.P. the edges of the ba se are equally inclined to the V.P. The prism is cut by an A.I.P. passing through the mid point of t he axis in such a way that the true shape of the section is a rhombus having diagonals of 100 mm and 50 mm. Draw the projections and determine the inclination of A.I.P. with the H.P. Here we are not given side of base of square prism. But the shorter diagonal of the rhombus will be equal to base diagonal of the prism. So to begin with, draw a square in the top view with base diagonal 50 mm. X Y 50 a b c d 110 The inclination of the cutting plane decides the length of longer diagonal. From the mid point of the axis cut two arcs of 50 m m radius, one on long edge ‘b’ and the other on the long edge ‘d’ X1 Y1 11 21 41 31 1 1’ 2’ 4’ 3’ 2 3 4
  • 29. Problem: A cone, diameter of the base 60 mm and axis 70 mm long is resting on its base on the H.P. It is cut by an A.I.P. so that the true shape of the section is an isosceles triangle having 50 m m base. Draw the plan, the elevation and the true shape of the section. X Y 70 60 25 25 o’ o a b a’ b’ o1 a1 b1
  • 30. 6 45 55 Problem: A cone, base 45 mm diameter and axis 55 mm long is resting on the H.P. on its base. It is cut by a section plane, perpendicular to both the H.P. and the V.P. and 6 mm away from the axi s. Draw its front view, top view and sectional side view.