1) The document describes various geometric solids and their projections including prisms, pyramids, cylinders, cones, and frustums. 2) It provides examples of different solids placed in various positions and orientations and outlines the step-by-step process to draw their projections. 3) The examples illustrate how to draw projections when axes of solids are inclined to the planes of projection at various angles and when parts of solids intersect projection planes.

4. Edge
Axis
Faces
Square
Prism
Pentagonal
Prism
Hexagonal
Prism
Triangular Prism

5. Edge
Base
Axis
SquarePyramid
Triangular Pyramid
Pentagonal Pyramid
Hexagonal Pyramid

6. (B) Solids of Revolutions:

7. Rectangle
Axis
Base

8. Right angle
triangle
Axis
Base
Generators

9. Axis
Base
Axis
Base

11. c’,3’b’,2’
A:- Axis perpendicular to V.P. and hence
parallel to both H.P. & P.P.
f’,6’
a
e’,5’
d’,4’a’,1’
b,f c,e d
43,52,61X Y
H

14. A cube of 50 mm long edges is so placed on
HP on one corner that a body diagonal is
parallel to HP and perpendicular to VP Draw
it’s projections.

15. Steps :
1.Assuming standing on HP, begin with TV,a square with all
sides
equally inclined to XY. Project FV and name all points of FV
& TV.
2.Draw a body-diagonal joining c’ with 1’( This can become //
to xy)
3.From 3’ drop a perpendicular on this and name it p’
4.Draw 2nd Fv in which 3’p’ line is vertical means c’-1’
diagonal
must be horizontal. .Now as usual project TV..
6.In final TV draw same diagonal is perpendicular to VP as
said in problem.
Then as usual project final FV.

16. 60
C 3
a 1
B 2
D 4
3’ 2’4’ 1’
C’
B’D’ A’
3’
2’4’
1’
C’
B’D’
A’
1
4d
c 3 a
b
2
c
b
1
4
d 3
2
3’
2’
B’
A’
D’
4’
C’ 1’P’

17. A pentagonal prism side of base 50 mm & axis
height 80 mm is held on a corner of its base
on HP such that the opposite rectangular face
appears to be a square in plan draw the
projection of prism when the vertical edge
containing that corner is inclined at to VP.
find the inclination of the prism with HP. The
top pentagonal faces of the prism is towards
the observer

19. A Hexagonal pyramid, side of base 30 mm
and axis length 70 mm is resting on the H.P.
on one of its base edges in such way that
its apex is 55 mm above H.P. Draw the
Projection of pyramid when the base edge
which is on the H.P. is parallel to V.P. Keep
apex of the solid on V.P.

20. • Initial position:
 Step 1:Since an edge of the base of the pyramid is on H . P.,
initially we will keep the base of the pyramid on H.P. with a side of
base perpendicular to V.P.(i.e. XY)
 Step 2:Draw the hexagon of side 30 mm in the T.V. with side ab
perpendicular to XY line. Projection the F.V.
• Intermediate position:
 Step 1:Apex of the pyramid must be 55 mm above H.P.Hence
redraw the F.V. of initial stage keeping d’e’ on the XY line and apex
o’ 55 mm above XY line.
 Step 2:Project various points of the F.V. vertically down and
project the points of initial stage T.V. parallel to XY line and to the
right to locate same point in second stage T.V.
 Step 3:Join the points in proper sequence following the rules of
visibility and non-visibility.

21. Final position:
 Step 1:Apex of the pyramid is kept on V.P. of side 30
mm in elevation, base edge ef must be parallel to V.P.
redraw the T.V. of intermediate stage with base edge
ef parallel to XY line.
 Step 2:Project the points from final stage T.V.
vertically up and project the points from
intermediate stage F.V. parallel to the XY line and to
the right to locate the points in the final stage F.V.
 Step 3: Join the points in proper sequence following
the rules of visibility and non-visibility.

23. Problem:5
A triangular pyramid side of base 30 mm
& axis height 60 mm is freely suspended
from midpoint of one of its slant edge.
Draw the projection of pyramid when
axis is inclined at 20˚ to VP.

24. Step 1: Pyramid is freely suspended from mid-point ‘P’ of
slant edge .We will assume the base of the pyramid on
HP in such a way that slant edge oc should be parallel
to VP.
Step 2: Draw an equilateral triangle of side 30 mm in the
TV with TV of slant edge parallel to XY line. Project the
FV locate the C.G. of the pyramid on the axis o’ s’ as g’.
15 mm above the base also locate point P’ on the mid-
point of slant edge o’ c’ , joint p’ to g’.
Step 3: Redraw the FV of initial stage by keeping p’g’
perpendicular to XY line. Care should be taken that no
part of the FV of intermediate stage is touching the XY
line as pyramid is freely suspended.

25. Step 4: project various point from FV vertically down and
project points of initial stage TV parallel to the XY Line and
to the right to locate same points in second stage TV.
Step 5: Joint the point in proper sequence following the rules
the visibility and non- visibility.
Step 6: Axis of the pyramid os is making an angle of 20˚ with
the VP but it is seen in apparent length in the TV
Hence we will calculate βos Redraw the TV of
intermediate stage with plan of axis os making βos with the
XY line.
Step 7: project the points from final stage TV vertically up
and project the points intermediate stage FV
???parallel??? to XY line and to the right to locate the
points in the final stage FV.
Step 8 : Joint the point in proper sequence following the
rules the visibility and non- visibility.

26. c’
c
o’
a’(b’)
p’
g’
s’
a
b
g,po,s
c’
o’
g’
p’
a’(b’)
s’
c₁
a₁
b₁
o₁g₁,p₁s₁
c₁’
a₁’
c₁
a₁
b₁
o₁
b₁’
o₁’
X Y

29. Problem No : 9
A right cylinder of 50 mm diameter &
100 mm length. Draw the projection
when it’s axis is inclined at angle of 50
to H.P. And 17 to V.P.

30. 1
0
0
R=25
50
17
Ɓ
Q-9
Locus of o
o

31. Problem No : 10
A frustum of a cone, having bottom
base diameter 70 mm top base
diameter and axis is 50 mm long is
resting on one of its generator on the
ground. Its axis is inclined at 45˚ to VP.
Draw its projections.