ENGINEERING GRAPHICS BRIDGE COURSE.pptx

KONGUNADUCOLLEGEOF ENGINEERING& TECHNOLOGY
(AUTONOMOUS)
DEPARTMENTOF SCIENCEAND HUMANITIES
20GE102-ENGINEERING GRAPHICS
FACULTY NAME : Mr.D.DHAVASHANKARAN
AP/CIVIL

Engineering Graphics
What is Engineering Graphics?
What is an Engineering Drawing?
A drawing that communicates an idea or design.
A set of rules and guidelines that help you
create an Engineering Drawing.

Engineering Graphics
Examples of Engineering Drawings
Mechanical Engineers
Detailed drawing of a part that needs to be
machined.
Electrical Engineers
A circuit schematic.
Circuit board layout.
Civil Engineers
Plans for a bridge.
Road layout.

A picture/drawing is worth a
thousand words..

DRAWING
Describing any object / information
diagrammatically is called drawing

Difference between drawing and
Engineering drawing

Engineering drawing
• Engineering drawing – A drawing of an object
that contains all information
like
• actual shape
• accurate size
• Dimensions, etc.,

Universal language
• Drawings prepared in one country may be
utilised in any other country irrespective of the
language spoken.
• Hence, engineering graphics is called the
universal language of engineers

Engineering Drawing
Manual Drawing CAD Software
Why we go for manualdrawing?
If basic fundamentals are clear, better use can be made of
the power of the software.
To be an expert in technical drawing, this first course on
Engineering (manual) Drawing is the first step.

Role of engineering graphics
• The ability to read drawing is the most important
requirement of all technical people in any profession as
compared to verbal or written description
• The subject in general is designed to
impart the following skills.
1. Ability to read and prepare engineering drawings.
2. Ability to make free - hand sketching of objects.
3. Power to imagine, analyse and communicate, and
4. Capacity to understand other subjects.

Applications of engineering
drawing
• Building drawing for civilengineers
• Machine drawing for mechanicalengineers
• Circuit diagrams for electrical and electronics
engineers

• How to start drawing ?
• What are all the instruments required
to drawing?
• What are all the specifications of
instruments?
• How to letter and dimension the drawing?

Instruments for Drawing
The following drawing instruments are required for preparing a neat and
correct drawing.
(a) Basic Instruments.
• Drawing board
• Drawing sheet
• Drawing pencil
• Drawing clips or pins
• Eraser
• Eraser shield
(b) Instruments for Drawing Straight Lines.
• T- square.
• Set- squares

c) Instruments for Drawing Curved Lines.
• Large size compass
• Small bow compass
• French curve
(d) Instruments for Measuring Distance.
• Large size divider
• Small bow divider
• Scales
(e) Instruments for MeasuringAngles.
• Protractors
• Set-squares
(f) SpecialTool.
• Mini drafter

Basics instruments
Drawing board
• A drawing board with its working surface
upward as shown in fig.1
• The top surface of the board is perfectly
smooth and level.
• Fig. 2 shows the bottom of the drawing
board. A drawing board is rectangular in
shape and is made of well seasoned soft
wood such as oak or pine

Sizes of drawing board
Last two sizes are normally used for student drawing

Drawing sheet
The drawing is frequently made in pencil on the
drawing sheet. The best drawing sheet has the
following qualities:
• Light cream buff in colour to have good
appearance
• Fine grains to pick up the graphite and produce
clean, dense blacklines
• Superior erasingqualities
• Folding strength
• Toughness
• Smooth surface

Pencils to be used
• Pencils with leads of different degrees of hardness or grades
are available in the market.
• The hardness or softness of the lead is indicated by 3H, 2H, H,
HB, B, 2B, 3B, etc.
• Wooden pencils – are graded and designated by numbers and
letters
• Mechanical clutch pencils – Not allowed
• 7B, 6B, 5B, 4B, 3B, 2B, B - in decreasing order of softness
and blackness
• HB to F – Medium grade
• H, 2H, 3H, 4H, 5H, 6H, 7H, 8H, 9H – increasing order of
hardness.

Grades and designations of
pencil
Drawings are done using 2H pencils and finished with H and HB pencils – to be
practiced in thiscourse.

Instruments for drawing
straight lines
T- square
•It is composed of a long strip called blade,
which is screwed rigidly at right angle to a
shorter piece called head or stock.
•It is made of mahogany or pear wood,
which is harder than the board wood.
•T- Square is used for making horizontal,
vertical, inclined or parallel lines on the
drawing sheet.

Instruments required for
measuring
• Dividers are used to divide straight or curved
lines into desired number of equal parts
Large Size Divider.
• The dividers has two legs hinged at the upper
end and is provided with steel pins at both the
lower ends, but it does not have the knee joints

Small Bow
Divider.
Large Size
Divider.

scales
• Scales are made of wood,
steel, celluloid or plastic
• Stainless steel scales are more durable
• Scale may be flat or of triangular
cross- section.
• 15 cm long and 2 cm wide or 30 cm long
or 3 cm wide flat scales are commonly
used

Protractor
• Protractors or Pro-circles are used for drawing
any desired angle.
• These are made of hard transparent plastic.
• The edges are either squared or beveled

Procedure to use mini draughter
• Set the protractor head with reference mark indexing zero
degree.
• A T-square, protractor and set squares can be replaced by a
drawing drafter. With this, lines can be drawn at any desired
angle.
• A mini drafter is made with several links. The scale is attached
at the working end of the links. The scale unit can be rotated
and set at any desired angle.
• The clamp end is fixed to the upper or lower edge of the
drawing board.
• There is no need to have a working edge on a drawing board
when a mini drafter isused.
• Place the drawing sheet underneath the scales of the mini-
drafter,
• Mini drafter saves considerable time.

Lettering
Lettering:
• Writing of titles, dimensions, notes and other important particulars on a drawing is
called lettering
• Lettering is the most important part of a drawing. Sometimes accurate and neat
drawing is spoiled by poor lettering. Therefore lettering should be done properly in
clear, legible and uniformstyle
• It should be in plain and simple style so that it could be done freehand and speedily.
• There are several ways in which lettering can be done. These include both hand
lettering and mechanicallettering
• Hand lettering practice is universal and always of value

Sizes of the letter
• Lettering should be in CAPITAL letters (upper cases)
• Lower cases used only for abbreviations like, mm , cm
etc..,
• Size of Letters is measured by the height h of the
CAPITAL letters as well as numerals.
• Standard heights for CAPITAL letters and numerals
recommended by BIS are given below :
• 1.8, 2.5, 3.5, 5, 6, 10, 14 and 20 mm
• Note: Size of the letters may be selected based upon the
size of drawing.

Dimensioning:
• An engineering drawing should contain the
details regarding the sizes, besides giving the
shape of an object.
• Dimension is a numerical value expressed in
appropriate units of measurement and marked
on a drawing with lines, symbols and notes.
• The dimensions without any unit is considered
in mm

TYPES OF LINES AND ITS APPLICATIONS

CONIC SECTIONS
ELLIPSE, PARABOLAAND HYPERBOLAARE CALLED
CONIC SECTIONS
BECAUSE
THESE CURVES APPEAR ON THE SURFACE
OF A CONE WHEN IT IS CUT BY SOME
TYPICAL CUTTING PLANES.
Section Plane
Through Generators
Ellipse
Section PlaneParallel
to end generator.
SectionPlane
Parallel toAxis.
Hyperbola

• TYPES OF ORTHOGRAPHIC
PROJECTION The following are the
types of orthographic projections.
• First angle projection
• Second angle projection
• Third angle projection
• Fourth angle projection
• In engineering drawing we are preferring only
the first angle projection.

• Isometric projection is a method for
visually representing three-dimensional
objects in two dimensions in technical and
engineering drawings.

1. SECTIONS OF SOLIDS.
2. DEVELOPMENT.
3. INTERSECTIONS.
ENGINEERING APPLICATIONS
OF
THE PRINCIPLES
OF
PROJECTIONS OF SOLIDES.
STUDY CAREFULLY
THE ILLUSTRATIONS GIVEN ON
NEXT SIX PAGES !

SECTIONING A SOLID.
An object ( here a solid ) is cut by
some imaginary cutting plane
to understand internal details 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, the part towards observer
is assumed to be removed.
2. As far as possible the smaller part is
assumed to be removed.
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.

DEVELOPMENT OF SURFACES OF SOLIDS.
MEANING:-
ASSUME OBJECT HOLLOW AND MADE-UP OF THIN SHEET. CUT OPEN IT FROM ONE SIDE AND
UNFOLD THE SHEET COMPLETELY. THEN THE SHAPE OF THAT UNFOLDED SHEET IS CALLED
DEVELOPMENT OF LATERLAL SUEFACES OF THAT OBJECT OR SOLID.
LATERLAL SURFACE IS THE SURFACE EXCLUDING SOLID’S TOP & BASE.
ENGINEERING APLICATION:
THERE ARE SO MANY PRODUCTS OR OBJECTS WHICH ARE DIFFICULT TO MANUFACTURE BY
CONVENTIONAL MANUFACTURING PROCESSES, BECAUSE OF THEIR SHAPES AND SIZES.
THOSE ARE FABRICATED IN SHEET METAL INDUSTRY BY USING
DEVELOPMENT TECHNIQUE. THERE IS A VAST RANGE OF SUCH OBJECTS.
EXAMPLES:-
Boiler Shells & chimneys, Pressure Vessels, Shovels, Trays, Boxes & Cartons, Feeding Hoppers,
Large Pipe sections, Body & Parts of automotives, Ships, Aeroplanes and many more.
WHAT IS
OUR OBJECTIVE
IN THIS TOPIC ?
To learn methods of development of surfaces of
different solids, their sections and frustums.
1. Development is different drawing than PROJECTIONS.
2. It is a shape showing AREA, means it’s a 2-D plain drawing.
3. Hence all dimensions of it must be TRUE dimensions.
4. As it is representing shape of an un-folded sheet, no edges can remain hidden
And hence DOTTED LINES are never shown on development.
But before going ahead,
note following
Important points.
Study illustrations given on next page carefully.

D
H
D
S
S
H

 = R
L
3600
R=Base circle radius.
L=Slant height.
L= Slant edge.
S = Edge of base
H= Height S = Edge of base
H= Height D= base diameter
Development of lateral surfaces of different solids.
(Lateral surface is the surface excluding top & base)
Prisms: No.of Rectangles
Cylinder: A Rectangle
Cone: (Sector of circle) Pyramids: (No.of triangles)
Tetrahedron: Four Equilateral Triangles
All sides
equal in length
Cube: Six Squares.


 = R
L
3600
R= Base circle radius of cone
L= Slant height of cone
L1 = Slant height of cut part.
Base side
Top side
L= Slant edge of pyramid
L1 = Slant edge of cut part.
DEVELOPMENT OF
FRUSTUM OF CONE
DEVELOPMENT OF
FRUSTUM OF SQUARE PYRAMID
STUDY NEXT NINE PROBLEMS OF
SECTIONS & DEVELOPMENT
FRUSTUMS

X Y
X1
Y1
A
B
C
E
D
a
e
d
b
c
A B C D E A
DEVELOPMENT
a”
b”
c”
d”
e”
Problem 1: A pentagonal prism , 30 mm base side & 50 mm axis
is standing on Hp on it’s base with one side of the base perpendicular to VP.
It is cut by a section plane inclined at 45º to the HP, through mid point of axis.
Draw Fv, sec.Tv & sec. Side view. Also draw true shape of section and
Development of surface of remaining solid.
Solution Steps:for sectional views:
Draw three views of standing prism.
Locate sec.plane in Fv as described.
Project points where edges are getting
Cut on Tv & Sv as shown in illustration.
Join those points in sequence and show
Section lines in it.
Make remaining part of solid dark.
For True Shape:
Draw x1y1 // to sec. plane
Draw projectors on it from
cut points.
Mark distances of points
of Sectioned part from Tv,
on above projectors from
x1y1 and join in sequence.
Draw section lines in it.
It is required true shape.
For Development:
Draw development of entire solid. Name from
cut-open edge I.e. A. in sequence as shown.
Mark the cut points on respective edges.
Join them in sequence in st. lines.
Make existing parts dev.dark.

Y
h
a
b
c
d
e
g
f
X a’ b’ d’ e’
c’ g’ f’
h’
o’
X1
Y1
g” h”f” a”e” b”d” c”
A
B
C
D
E
F
A
G
H
SECTIONAL T.V
SECTIONAL S.V
DEVELOPMENT
Problem 2: A cone, 50 mm base diameter and 70 mm axis is
standing on it’s base on Hp. It cut by a section plane 450 inclined
to Hp through base end of end generator.Draw projections,
sectional views, true shape of section and development of surfaces
of remaining solid.
Solution Steps:for sectional views:
Draw three views of standing cone.
Locate sec.plane in Fv as described.
Project points where generators are
getting Cut on Tv & Sv as shown in
illustration.Join those points in
sequence and show Section lines in it.
Make remaining part of solid dark.
For True Shape:
Draw x1y1 // to sec. plane
Draw projectors on it from
cut points.
Mark distances of points
of Sectioned part from Tv,
on above projectors from
x1y1 and join in sequence.
Draw section lines in it.
It is required true shape.
For Development:
Draw development of entire solid.
Name from cut-open edge i.e. A.
in sequence as shown.Mark the cut
points on respective edges.
Join them in sequence in curvature.
Make existing parts dev.dark.

X Y
e’
a’ b’ d’
c’ g’ f’
h’
o’
o’
Problem 3: A cone 40mm diameter and 50 mm axis is resting on one generator on Hp( lying on Hp) which is // to
Vp.. Draw it’s projections.It is cut by a horizontal section plane through it’s base center. Draw sectional TV,
development of the surface of the remaining part of cone.
A
B
C
D
E
F
A
G
H
O
a1
h1
g1
f1
e1
d1
c1
b1
o1
SECTIONAL T.V
DEVELOPMENT
(SHOWING TRUE SHAPE OF SECTION)
HORIZONTAL
SECTION PLANE
h
a
b
c
d
e
g
f
O
Follow similar solution steps for Sec.views - True shape – Development as per previous problem!

A.V.P300 inclined to Vp
Through mid-point of axis.
X Y
1
2
3 4
5
6
7
8
b’ f’
a’ e’
c’ d’
a
b
c
d
e
f
a1
d1
b1
e1
c1
f1
X1
Y1
AS SECTION PLANE IS IN T.V.,
CUT OPEN FROM BOUNDRY EDGE C1 FOR DEVELOPMENT.
C D E F A B C
DEVELOPMENT
SECTIONAL F.V.
Problem 4: A hexagonal prism. 30 mm base side &
55 mm axis is lying on Hp on it’s rect.face with axis
// to Vp. It is cut by a section plane normal to Hp and
300 inclined to Vp bisecting axis.
Draw sec. Views, true shape & development.
Use similar steps for sec.views & true shape.
NOTE: for development, always cut open object from
From an edge in the boundary of the view in which
sec.plane appears as a line.
Here it is Tv and in boundary, there is c1 edge.Hence
it is opened from c and named C,D,E,F,A,B,C.
Note the steps to locate
Points 1, 2 , 5, 6 in sec.Fv:
Those are transferred to
1st TV, then to 1st Fv and
Then on 2nd Fv.

1’
2’
3’
4’
5’
6’
7’
7
1
5
4
3
2
6
7
1
6
5
4
3
2
a
b
c
d
e
f
g
4
4 5
3
6
2
7
1
A
B
C
D
E
A
F
G
O
O’
d’e’ c’f’ g’b’ a’
X Y
X1
Y1
F.V.
SECTIONAL
TOP VIEW.
Problem 5:A solid composed of a half-cone and half- hexagonal pyramid is
shown in figure.It is cut by a section plane 450 inclined to Hp, passing through
mid-point of axis.Draw F.v., sectional T.v.,true shape of section and
development of remaining part of the solid.
( take radius of cone and each side of hexagon 30mm long and axis 70mm.)
Note:
Fv & TV 8f two solids
sandwiched
Section lines style in both:
Development of
half cone & half pyramid:

o’
h
a
b
c
d
g
f
o e
a’ b’ c’ g’ d’f’ e’
h’
X Y
 = R
L
3600
L=Slant height.

A
B
C
D
E
F
G
H
A
O
1
3
2
4
7
6
5
L
1
2
3
4
5
6
7
1’
2’
3’ 4’
5’
6’
7’
Problem 6: Draw a semicircle 0f 100 mm diameter and inscribe in it a largest
circle.If the semicircle is development of a cone and inscribed circle is some
curve on it, then draw the projections of cone showing that curve.
Solution Steps:
Draw semicircle of given diameter, divide it in 8 Parts and inscribe in it
a largest circle as shown.Name intersecting points 1, 2, 3 etc.
Semicircle being dev.of a cone it’s radius is slant height of cone.( L )
Then using above formula find R of base of cone. Using this data
draw Fv & Tv of cone and form 8 generators and name.
Take o -1 distance from dev.,mark on TL i.e.o’a’ on Fv & bring on o’b’
and name 1’ Similarly locate all points on Fv. Then project all on Tv
on respective generators and join by smooth curve.
TO DRAW PRINCIPAL
VIEWS FROM GIVEN
DEVELOPMENT.

h
a
b
c
d
g
f
e
o’
a’ b’ d’
c’ g’ f’
h’ e’
X Y
A
B
C
D
E
F
G
H
A
O L
 = R
L
3600
L=Slant height.

1’
2’ 3’
4’
5’
6’
7’
1
2
3
4
5
6
7
Problem 7:Draw a semicircle 0f 100 mm diameter and inscribe in it a largest
rhombus.If the semicircle is development of a cone and rhombus is some curve
on it, then draw the projections of cone showing that curve.
TO DRAW PRINCIPAL
VIEWS FROM GIVEN
DEVELOPMENT.
Solution Steps:
Similar to previous
Problem:

a’ b’ c’ d’
o’
e’
a
b
c
d
o e
X Y
A
B
C
D
E
A
O
2
3
4
1
Problem 8: A half cone of 50 mm base diameter, 70 mm axis, is standing on it’s half base on HP with it’s flat face
parallel and nearer to VP.An inextensible string is wound round it’s surface from one point of base circle and
brought back to the same point.If the string is of shortest length, find it and show it on the projections of the cone.
1 2
3
4
1’
2’ 3’ 4’
TO DRAW A CURVE ON
PRINCIPAL VIEWS
FROM DEVELOPMENT. Concept: A string wound
from a point up to the same
Point, of shortest length
Must appear st. line on it’s
Development.
Solution steps:
Hence draw development,
Name it as usual and join
A to A This is shortest
Length of that string.
Further steps are as usual.
On dev. Name the points of
Intersections of this line with
Different generators.Bring
Those on Fv & Tv and join
by smooth curves.
Draw 4’ a’ part of string dotted
As it is on back side of cone.

X Y
e’
a’ b’ d’
c’ g’ f’
h’
o’
h
a
b
c
d
e
g
f
O
DEVELOPMENT
A
B
C
D
E
F
A
G
H
O
1
2
3
4
6 5
7
1’
2’
3’
4’
5’
6’
7’
1
2
3
4
5
6
7
HELIX CURVE
Problem 9: A particle which is initially on base circle of a cone, standing
on Hp, moves upwards and reaches apex in one complete turn around the cone.
Draw it’s path on projections of cone as well as on it’s development.
Take base circle diameter 50 mm and axis 70 mm long.
It’s a construction of curve
Helix of one turn on cone:
Draw Fv & Tv & dev.as usual
On all form generators & name.
Construction of curve Helix::
Show 8 generators on both views
Divide axis also in same parts.
Draw horizontal lines from those
points on both end generators.
1’ is a point where first horizontal
Line & gen. b’o’ intersect.
2’ is a point where second horiz.
Line & gen. c’o’ intersect.
In this way locate all points on Fv.
Project all on Tv.Join in curvature.
For Development:
Then taking each points true
Distance From resp.generator
from apex, Mark on development
& join.

X Y
1
2
3
4
5
6
7
8
9
10
11
12
Q 15.26: draw the projections of a cone resting on the ground on its base and show on them, the shortest path
by which a point P, starting from a point on the circumference of the base and moving around the cone will
return to the same point. Base ofn cone 65 mm diameter ; axis 75 mm long.
1
2
12
3
11
4
10
5
9
6
8 7
2
3
4
5
6
7
8
9
10
11
12
1
θ=141º

Q 15.26: A right circular cone base 30 mm side and height 50 mm rests on its base on H.P. It is cut by a
section plane perpendicular to the V.P., inclined at 45º to the H.P. and bisecting the axis. Draw the projections
of the truncated cone and develop its lateral surface.
X Y
1
2
3
4
5
6
7
8
9
10
11
12
1
2
12
3
11
4
10
5
9
6
8 7
2
3
4
5
6
7
8
9
10
11
12
1
a
b
c
k
d
e
f
g
h
i
l
j
a
f
b
c
k
d
e
g
h
i
l
j
A
C
D
E
B
A
F
G
H
I
J
K
L
θ=103º

Q 14.11: A square pyramid, base 40 mm side and axis 65 mm long, has its base on the HP and all
the edges of the base equally inclined 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. Also draw its development.
X
45º
a
b
c
d
o
a’
b’
c’
d’
o’
1
2
3
4
1’
2’
3’
4’
11
41
21 31
Y
A
B
C
D
A
O
1
1
2
3
4

Q 14.14: 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.
Y
X
a’ b’ e’ c’ d’
a
b
c
d
e
o
o’
60
c’d’ o’
a’
b’e’
30
a1
b1
c1
d1
e1
o1
1’
2’
3’
4’
5’
6’
1
2
3
4
5
6
31’
41’
21’
11’
61’
51’
O
A
B
C
D
E
A
1
2
3
4
5
6
1
5
6

Q 14.11: A square pyramid, base 40 mm side and axis 65 mm long, has its base on the HP with
two 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 and true shape of
the section. Also draw its development.
X
o’
Y
A
B
C
D
A
O
a b
c
d
o
a’ d’ b’ c’
1
2
3
4
1’ 4’
2’ 3’
2
3
1
2
True length
of slant edge
1 4
1
1
4
2 3
2
3
True length
of slant edge

Q.15.11: A right circular cylinder, base 50 mm diameter and axis 60 mm long, is standing on HP on its
base. It has a square hole of size 25 in it. The axis of the hole bisects the axis of the cylinder and is
perpendicular to the VP. The faces of the square hole are equally inclined with the HP. Draw its
projections and develop lateral surface of the cylinder.
Y
1
2
3
4
5
6
7
8
9
10
11
12
X
1’
2’
12’
3’
11’
4’
10’
5’
9’
6’
8’ 7’
a’
b’
c’
d’
1 2 3 4 5 6 7 8 9 10 11 12 1
a
a
b
d
b
d
c
c
A
B
D
C C
B
D
A
a c

Q.15.21: A frustum of square pyramid has its base 50 mm side, top 25 mm side and axis 75 mm. Draw
the development of its lateral surface. Also draw the projections of the frustum (when its axis is vertical
and a side of its base is parallel to the VP), showing the line joining the mid point of a top edge of one
face with the mid point of the bottom edge of the opposite face, by the shortest distance.
Y
X
50 25
75
a b
c
d
a1 b1
c1
d1
a’
d’
b’
c’
a1’
d1’
b1’
c1’
o
o’
True
length of
slant edge
A1
B1
C1
D1
A1
A
B
C
D
A
P
Q
R
S
p’
p
q’
q
r’
r
s’
s

Q: A square prism of 40 mm edge of the base and 65 mm height stands on its base on the HP with
vertical faces inclined at 45º with the VP. A horizontal hole of 40 mm diameter is drilled centrally
through the prism such that the hole passes through the opposite vertical edges of the prism, draw
the development og the surfaces of the prism.
Y
X
a
b
c
d
a’ b’d’ c’
a’ b’d’ c’
1’
2’
3’
4’
5’
6’
7’
8’
9’
10’
11’
12’
1
1
2
12
2
12
3
11
3
11
4 10
4 10
5
9
5
9
4
8
4
8
1 2
12
3
11
4
10
A
B
C
7
7
5
9
6
8
7 6
8
5
9
4
10
7 1
2
12
3
11 A
1
2
12
11
3
10
4
9
5
8
6
7 1
2
12
11 9
5
8
7
3
4
6
10
D

ENGINEERING GRAPHICS BRIDGE COURSE.pptx

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