X
Y
V T
YX
No HT for this CP
TYPES OF SECTION PLANES
SECTION PLANE / CUTTING PLANE
Parallel to HP & Perpendicular to VP
X
Y
SECTION PLANE / CUTTING PLANE
Perpendicular to HP & Parallel to VP
TYPES OF SECTION PLANES
H T
YX
No VT for this CP
X
Y
θθ(cp)
V
H
TYX
φ (cp) = 900
┐
TYPES OF SECTION PLANES
SECTION PLANE / CUTTING PLANE
Inclined to HP & Perpendicular to VP
X
YCutting plane
φ
φ(cp)
V
H
TYX
TYPES OF SECTION PLANES
SECTION PLANE / CUTTING PLANE
Perpendicular to HP & Inclined to VP
θ (cp) = 900┐
X
Y
H
TYX
V
SECTION PLANE / CUTTING PLANE
Perpendicular to HP & Perpendicular to VP
X
Y
X
Y
X
Y
X
Y
X
Y
φ
Cutting plane.Inclined to VP
A square pyramid 50 mm base side and axis 90 mm
long is resting on HP at its base with a side of base
parallel to VP. The pyramid is cut by a section plane
parallel to HP and perpendicular to VP, bisecting the
axis. Draw the sectional views and the true shape of
the section.
Sections of solids – Q1
Sections of solids – Q1
X Y
V T
a
bc
d
o
o’
a’,b’c’,d’
1’, 2’3’,4’
1
23
4
FV of the Section
TV of the Section & True shape of the section
Sections of solids – Q1
CP Ʇ to VP →Sectional FV is a straight line.
CP ‖ to HP → Sectional TV is a closed figure &is the True shape of the section
A square pyramid 50 mm base side and axis 90 mm
long is resting on HP at its base with a side of base
parallel to VP. The pyramid is cut by a section plane
inclined at 45° to HP and perpendicular to VP, bisecting
the axis. Draw the sectional views and the true shape
of the section.
Sections of solids – Q2
CP Ʇ to VP → Sectional FV is a straight line.
CP Inclined to HP → Sectional TV is a closed figure,but not the True shape of the section.
X
V
T
a
bc
d
o
o’
a’,b’c’,d’
1’, 2’
3’,4’
1
23
4
FV of the Section
TV of the Section
) Θ(CP)
V
T
H
Y
X
┘
41
31
21
11
Y1
X1
H
Y
True Shape of Section
Sections of solids – Q2
CP perpendicular to VP & inclined to HP
(1). Sectional FV is a Straight Line.
(2). Sectional TV is a Closed Figure.
(3). True Shape is similar to Sectional TV, but enlarged.
Distance of New Plan points from X1 Y1
= Distance of Old Plan points from XY.
A square pyramid 60 mm base side and axis 90
mm long is resting on HP at its base. The pyramid
is cut by a section plane in such away that the
true shape of the section is a trapezium with
parallel sides 40mm and 20 mm. Draw the FV and
TV showing the section. Also show the true shape
of the section.
Sections of solids – Q3
a
bc
d
o
X Y
V
T
H
o’
a’,b’c’,d’
1’, 2’
3’,4’
1
23
4
FV of the Section
TV of the Section
) θ(CP) = ?
X1
Y1
11
21
31
41
True Shape of the Section
Sections of solids – Q3
10
A square pyramid 40 mm base side and axis 65 mm
long its base on HP and all the edges of base are
equally inclined to the VP. It is cut by section plane
perpendicular to VP, inclined at 45° to HP and
bisecting the axis. . Draw its front view, sectional
top view, sectional side view and true shape of the
section.
Sections of solids – Q4
CP Ʇ to VP → Sectional FV is a straight line.
CP Inclined to HP → Sectional TV is a closed figure,but not the True shape of the section.
YX
a
b
c
d
o
o’
a’c’ b’, d’
V
T
H
X1
Y1
13
4
2
1’2’,4’
3’
11
21
31
41
θ (cp) (
Sections of solids – Q4
Sections of solids – Q4
A cone is resting on its base on HP. It is cut by aplane inclined 45° to HP and perpendicular to VP.
It cuts the axis of the cone at a point 40 mmbelow the vertex. Draw the front view, sectionaltop view and the true shape of the section, if the
diameter of the cone base is 80 mm and thelength of the axis is 90 mm.
Sections of solids – Q5
CP Ʇ to VP → Sectional FV is a straight line.
CP Inclined to HP → Sectional TV is a closed figure,but not the True shape of the section.
1
2
3
4
5
6
7
8
o
1’5’
0’
2’,8’3’,7’4’,6’
V
TX Yθ(cp)
H
Y1
X1
Sections of solids – Q5
A cone of base diameter 120 mm and height 135
mm is resting on HP on its base. It is cut by an
inclined HP such that the true shape obtained is an
ellipse whose major axis is 100 mm long. Draw the
projections of cone showing sectional views and
the true shape of the section.
Sections of solids – Q6
1
2
3
4
5
6
7
8
o
1’5’
0’
2’,8’3’,7’4’,6’
V
TX Yθ(cp)
H
Y1
X1
Sections of solids – Q6
A cone base 60 mm diameter and axis 70 mm
stands vertically with its base on HP. The vertical
trace of a section plane perpendicular to VP and
parallel to one of the end generators of the cone
passes at a distance of 15 mm from it. Draw the
sectional plan and the true shape of the section.
Sections of solids – Q7
1’5’
0’
2’,8’3’,7’4’,6’
V
TX Y
H
Sections of solids – Q7
1
2
3
4
5
6
7
8
o
Y1
X1
Chord length in the sectional TV =Base length (maximum double ordinate) in the true shape.
i.e. AB = A1B1
A
B
A cone base 60 mm diameter and axis 90 mm stands
vertically with its base on HP. It is cut by a section
plane such that the true shape is a parabola of
maximum double ordinate of 50 mm. Draw the
projections of the cone showing sectional views and
the true shape of the section.
Sections of solids – Q8
Cone Fully defined. Parabola Not Fully defined.
1’5’
0’
2’,8’3’,7’4’,6’
V
TX Y
H
Sections of solids – Q8
1
2
3
4
5
6
7
8
o
Y1
X1
Chord length in the sectional TV =Base length (maximum double ordinate) in the true shape.
i.e. AB = A1B1
A
B
50
A cone base 60 mm diameter standing up right is
cut by a section plane such that the true shape is
a parabola of maximum double ordinate of 50
mm. and the vertex being 70 mm from this
ordinate. Draw the front view, sectional top view
and true shape of the section. What is the
inclination of the section plane?
Sections of solids – Q9
Cone Not Fully defined. Parabola Fully defined.
1’5’
0’
2’,8’3’,7’4’,6’
V
TX Y
H
Sections of solids – Q9
1
2
3
4
5
6
7
8
o
Y1
X1
Chord length in the sectional TV =Base length (maximum double ordinate) in the true shape.
i.e. AB = A1B1
A
B
50
Draw an isosceles with (1’- T) as base and 90mm as slant edges.
A cone of base diameter 50 mm and axis 60 mm
long is resting on HP on its base. It is cut by a
section plane such that the true shape is an
isosceles triangle of base 40 mm. Draw the
sectional views and the true shape of the section.
Sections of solids – Q10
X Y
1
2
3
4
5
6
7
8
o
1’5’
0’
2’,8’3’,7’4’,6’
V
T
H
40
X1
y1
Sections of solids – Q10
A cone of base diameter 50 mm and axis 55 mm
long is resting on HP on its base. It is cut by a
section plane perpendicular to both HP and VP
and 6mm away from the axis. Show the sectional
side view. Mark the height of the section.
Sections of solids – Q11
X Y
1
2
3
4
5
6
7
8
o
1’5’
0’
2’,8’3’,7’4’,6’
X1
y1
T
H
V
6p’
q’ r’
r
q
p
p1’
r1’q1’
a’,b’
a
b
a1’ b1’
Sections of solids – Q11
A cone of base diameter 60 mm and axis 75 mm
long is resting on HP on its base. It is cut by a section
plane such that the true shape is a hyperbola of
maximum double ordinate of 50 mm. Draw the
sectional views and the true shape of the section.
Sections of solids – Q12
X Y
1
2
3
4
5
6
7
8
o
1’5’
0’
2’,8’3’,7’4’,6’
X1
y1
T
H
V
6p’
q’ r’
r
q
p
p1’
r1’q1’
a’,b’
a
b
a1’ b1’
Sections of solids – Q11
50
A cone base 60 mm diameter and axis 90 mm
stands vertically with its base on HP. It is cut by a
vertical section plane inclined at 30° to VP and
passing through a point on the cone 10 mm off the
axis. Draw the sectional views and the true shape
of the section.
Sections of solids – Q13
X Y
1
2
3
4
5
6
7
8
o
1’5’
0’
2’,8’3’,7’4’,6’
Sections of solids – Q13
300
H
T
ab
cd
e
f
9
9’
300
Y1
X1
A cube of 50 mm side is cut by an inclined
plane such that the true shape obtained is a
regular hexagon. Draw the sectional views
and the true shape of the section.
Cube in Corner position.
VT throughMid points of top right half & bottom left half.
Sections of solids – Q14
X
Y
V
H
T
X1
Y1
p’, q’
r’, s’
t’, u’
p
q
r
s
u
t
a,1
b,2
c,3
d,4
a’c’ b’, d’
1’3’ 2’, 4’
p1
r1
u1
s1
q1
t1
Sections of solids – Q14
A cube of 35 mm side is cut by an inclined plane
such that the true shape obtained is an
equilateral triangle of maximum size. Draw the
sectional views and the true shape of the section.
Sections of solids – Q15
X
Y
V
H
T
X1
Y1
a,1
b,2
c,3
d,4
a’c’ b’, d’
1’3’ 2’, 4’Sections of solids – Q15
A cube of 40 mm side is cut by an inclined plane
such that the true shape obtained is a trapezium
of parallel sides equal to the length of the
diagonal of a square face for one side and half of
that length for the other side. Draw the sectional
views and the true shape of the section.
Sections of solids – Q16
X
Y
V
H
T
X1
Y1
a,1
b,2
c,3
d,4
a’c’ b’, d’
1’3’ 2’, 4’Sections of solids – Q16
A hexagonal pyramid, side of base 30 mm and
axis 60 mm long, is resting on its base on ground
with two base edges parallel to VP. It is cut by a
vertical plane inclined at 30° to VP and cutting
the pyramid 5 mm off the axis. Draw the top
view, sectional front view and the true shape of
the section.
Sections of solids – Q17
CP Ʇ to HP → Sectional TV is a straight line.
CP Inclined to VP → Sectional FV is a closed figure,but not the True shape of the section.
X Y
a
bc
d
e f
o
a’
O’
d’ b’, f’c’, e’
H
V
Tφ(cp)= 300
5
21
43
1’
2’
4’
5’
3’X1
Y1
Sections of solids – Q17
A pentagonal pyramid, side of base 30 mm and height 60
mm, is lying on one of its triangular faces on ground
with the axis parallel to the VP. The vertical trace of a
horizontal section plane passes through the centre of
the base of the pyramid. Draw the top view showing the
section.
Sections of solids – Q18
X
Y
a
b
c
d
e
o
a’,b’c’,e’d’
o’
c’,e’
a’,b’ o’
d’
o1
a1
c1
e1
d1
b1
V T1’,2’ 3’,4’ 5’
1’ on b’c’ & 2’ on e’a’
3’ on o’c’ & 4’ on o’e’
5’ on o’d’
1
2
3
4
5
Sections of solids – Q18
A pentagonal pyramid, side of base 30 mm
and height 60 mm, is lying on one of its
triangular faces on ground with the axis
parallel to the VP. A vertical section plane,
whose HT bisects the plan of the axis and
makes an angle of 30° with the reference
line, cuts the pyramid, removing its top
part. Draw the plan, sectional elevation
and true shape of the section.
Sections of solids – Q19
X Y
a
b
c
d
e
o
a’,b’c’,e’d’
o’
c’,e’
a’,b’ o’
d’
o1
a1
c1
e1
d1
b1
1 on b1c1 & 2 on c1d1
3 on o1b1 & 4 on o1d1
5 on o1a1 & 6 on o1e1
Sections of solids – Q19
12
3
45
6
1’
2’
3’
4’
5’
6’
300
H
T
X Y
o1
a1
c1
e1
d1
b1
Sections of solids – Q19 (continued)
12
3
45
6
300
H
T
c’,e’
a’,b’ o’
d’