TYPES OF SECTION PLANES V T X Y No HT for this CP SECTION …€¦ · A square pyramid 50 mm base...

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


Perpendicular to HP & Parallel to VP


H T

YX

No VT for this CP

X

Y

θθ(cp)

V

H

TYX

φ (cp) = 900

┐



Inclined to HP & Perpendicular to VP

X

YCutting plane

φ

φ(cp)

V

H

TYX



Perpendicular to HP & Inclined to VP

θ (cp) = 900┐

X

Y

H

TYX

V


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

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


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


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.


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


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.


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


10


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.




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) (


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.




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


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.


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


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.


1’5’

0’

2’,8’3’,7’4’,6’

V

TX Y

H


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.


Cone Fully defined. Parabola Not Fully defined.

1’5’

0’

2’,8’3’,7’4’,6’

V

TX Y

H


1

2

3

4

5

6

7

8

o

Y1

X1


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?


Cone Not Fully defined. Parabola Fully defined.

1’5’

0’

2’,8’3’,7’4’,6’

V

TX Y

H


1

2

3

4

5

6

7

8

o

Y1

X1


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.


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



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.


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’



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



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’


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.


X Y

1

2

3

4

5

6

7

8

o

1’5’

0’

2’,8’3’,7’4’,6’


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.


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


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



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.


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.


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


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.


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


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.


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


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’

TYPES OF SECTION PLANES V T X Y No HT for this CP SECTION …€¦ · A square pyramid 50 mm base...

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Transcript of TYPES OF SECTION PLANES V T X Y No HT for this CP SECTION …€¦ · A square pyramid 50 mm base...