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DEVELOPMENT OF SURFACES DR. R. VASUDEVAN
21st NOV 2007
NOTE – BOTH ARE ‘A’ D A
C
A
B
C
D
A
E
F
G
H
E
B H E
G F
CUT EDGE AE
D A
C
C
D
A
B
C
G
H
E
F
G
B H E
G F
CUT EDGE CG
IF CUT EDGE IS CG WHAT WILL BE 1 TO 10 – TEACHER EXPLAINS D A
C
1
2
3
4
5
6
7
8
9
10
B H E
G F
1 –C, 6- ,
2-D, 7-
3-A, 8-
4-B, 9-
5-C 10
EXERCISE -1 D A
C
1
2
3
4
5
6
7
8
9
10
B H E
G F
IF CUT EDGE IS BF WHAT LETTERS SHALL BE AT 1 TO 10 – WRITE ANSWERS
ANS TO EX - 1 D A
C
1
2
3
4
5
6
7
8
9
10
B H E
G F
1-B 6-F
2-C 7-G
3-D 8-H
4-A 9-E
5-B 10-F
IF CUT EDGE IS BF - ANSWERS
TOP FACE CAN BE ATTACHED TO AB OR BC OR CD OR DA D
D A
C
AA
C BB C
D
A
F
H
E
B H E
G F
E
G
TOP FACE ATTACHED TO ‘AB’
TOP FACE CAN BE ATTACHED TO AB OR BC OR CD OR DA B
D A
C
A
A
B CC
DD
A
E
F
H
E
B H E
G F
G
TOP FACE ATTACHED TO ‘CD’
TOP FACE CAN BE ATTACHED TO AB OR BC OR CD OR DA A D D A
C
A
BB
C
D
A
E
F
G
H
E
B H E
G F
TOP FACE ATTACHED TO ‘BC’
D
D A
C
AA
C BB C
D
A
H
E
B H E
G F
E
FF
G
E
H
NOTE CC EE HH
TOP FACE CAN BE ATTACHED TO AB OR BC OR CD OR DA D
D A
C
AA
C BB C
D
A
F
H
E
B H E
G F
E
G
TOP FACE ATTACHED TO ‘AB’
EXERCISE - 2 D
11
A
C
12 3 4
1 2
5
B H E
G F
6
7
8 13
9 14
IF CUT EDGE IS BF WHAT LETTERS SHALL BE AT 1 TO 14 – WRITE ANSWERS
10
ANS TO EX - 2 D
11
A
C
12 3 4
1 2
5
B H E
G F
6
7
8 13
9
10
14
IF CUT EDGE IS BF 1-B 2-C 3-D 4-A 5-B 11-B 6-F 7-G 8-H 9-E 10-F 13-G
12-A 14-F
ANS TO EX - 2 D
11
A
C
12 3 4
1 2
5
B H E
G F
F
G
H G
E
F
F
IF CUT EDGE IS BF 1-B 2-C 3-D 4-A 5-B 11-B 6-F 7-G 8-H 9-E 10-F 13-G
12-A 14-F
EXERCISE - 3 A
F B
E D C
L G H
10
1
2
12
13
9
11 3 4
8 5
6
7
K J I
14 15 16
17 22
19
IF CUT EDGE IS BH WHAT LETTERS SHALL BE AT 1 TO 22 – WRITE ANSWERS
20 21
18
ANS TO EX - 3 A
F B
E D C
L G H
10
1
2
12
13
9
11 3 4
8 5
6
7
K J I
14 15 16
17
18
22
19 20 21
IF CUT EDGE IS BH 1-B 2-C 3-D 4-E 5-F 6-A 7-B 8-A 9-B 10-C 11- D 12-H 13-I 14-J 15-K 16-L 17-G 18-H 22-H 21-I 20-J 19--K
EXERCISE - 4 1
7
C 4
A
6
5 3
2
4
B
F D
E
6
8
7
IF CUT EDGE IS AD WHAT LETTERS AT 1 TO 10 – WRITE ANSWERS
10
9
ANS TO EX - 4 1
7
C 4
A
6
5 3
2
4
B
F D
E
6
8
7
IF CUT EDGE IS AD 1-A 2-B 3-C 4-A 5-A 6-D 7-E 8-F 9-D 10-D
10
9
EXERCISE - 5 A
7
C 4
A
6
5 2
3
4
B
F D
E
D
7
8
9
WHAT IS THE CUT EDGE 10 WHAT IS LENGTH AB, BC, CD, DE, EF, FD
ANS TO EXERCISE - 5 A
7
C 4
A
6
5 3
2
4
B
F D
E
D
8
7 10
WHAT IS THE CUT EDGE AD AB-6, BC-7, CA-4, DE-6, EF-7, FD-4
9
IMAGINARY SURFACE LINES ARE CALLED SURFACE GENERATORS – GENERALLY 8 OR 12 SURFACE GENERATORS
PYRAMIDS
FACE EDGES TAPER TO A POINT
PRISMS
FACE EDGES VERTICAL
PYRAMIDS
FACE EDGES TAPER TO A POINT
O O
A B(C)
A(D) D A
O
C B
D
B C
O O
B(C)
D A
O
A
C B
D
A
B
A(D)
C
PRISMS
FACE EDGES VERTICAL
A(D)
B(C) D
A
B
C
D A
D
C B H
E(H) D(H) A(E)
E F(G) H C(G) B(F)
CUT EDGE DH
E
F
G
H
G F
D A(D)
B(C) D A
C B C
D A
D
C B H
E(H) D(H) A(E)
E F(G) H E C(G) H B(F)
CUT EDGE DH
F G G
H
G F
D
ΠD
ΠD/8 IMAGINARY SURFACE LINES ARE CALLED SURFACE GENERATORS – GENERALLY 8 OR 12 SURFACE GENERATORS
Exercise – 6 Draw the development of the surfaces of a rectangular prism of length 4 cm, width 3 cm, height 8 cm
DRAW VIEW FROM TOP (PLAN VIEW ), VIEW FROMFRONT(ELEVATION), TRANSFER WIDTHS FROM PLAN, HEIGHTS FROM ELEVATION A’(D’)
B’(C’) A
B
C
D
A
E’(H’) D(H)
F’(G’) E
F
G
H
E
A(E)
C(G)
B(F)
Exercise – 7 Draw the development of the surfaces of a pentagonal prism of side 3 cm, height 8 cm
DRAW VIEW FROM TOP (PLAN VIEW ), VIEW FROMFRONT(ELEVATION), TRANSFER WIDTHS FROM PLAN, HEIGHTS FROM ELEVATION
Exercise – 8 Draw the development of the surfaces of a triangular prism of side 3 cm, 4 cm , and 6 cm and height 8 cm
DRAW VIEW FROM TOP (PLAN VIEW ), VIEW FROMFRONT(ELEVATION), TRANSFER WIDTHS FROM PLAN, HEIGHTS FROM ELEVATION
Exercise – 9 Draw the development of the surfaces of a cylinder of radius 3.5 cm, and height 9 cm
TRANSFER THE WIDTHS WITH A PROTRACTOR OR BY CALCULATION. CIRCUMFERANCE= 2*PI*R =2*22/7* 3.5 = 22 CM. DIVIDE BY 8 = 2.75 CM
PYRAMIDS
FACE EDGES TAPER TO A POINT
IN PYRAMIDS EDGES WILL BE INCLINED TO BOTH THE PLANES, VP AND HP. THE STANDARD PROCEDURE TO GET TRUE LENGTH IS TO ROTATE THE LINES, AROUND VERTICAL AXIS WITH TOP POINT FIXED. THE BOTTOM POINT WILL REMAIN IN THE SAME HEIGHT AND HENCE THE LOCUS WILL BE PARALLEL TO XY LINE IN VP. IN HP WHEN LINE IS ROTATED PARALLEL TO XY, IT IS PARALLEL TO VP AND WILL SHOW REAL LENGTH
o b’ X
b
a’
a
o
Y
LINE OA IS INCLINED BOTH TO VP AND TO HP IN BOTH VIEWS, HENCE WILL NOT GIVE TRUE LENGTH O
O
B(C)
A(D) D A
O
A
C B
D
A B
C
TO GET TRUE LENGTH OF OA, ROTATE IN PLAN VIEW, SO THAT IT BECOMES PARALLEL TO VP O
O
B(C)
A(D) D A
O
A
C B
D
A B
C
AB, BC, CD, DA ARE LYING IN HP, HENCE ARE PARALLEL TO HP, AND HAVE TRUE LENGTHS IN VIEW FROM TOP O
O
B(C)
A(D) D A
O
A
C B
D
A B
C
Exercise – 10 Draw the development of the surfaces of a pyramid of base 8cm wide, 6 cm depth and height 9 cm
AB, BC, CD, DA ARE LYING IN HP, HENCE ARE PARALLEL TO HP, AND HAVE TRUE LENGTHS IN VIEW FROM TOP O
O
B(C)
A(D) D A
O
A
C B
D
A B
C
DEVELOPMENT OF CUT SURFACES DR. R. VASUDEVAN DIRECTOR / SET 12 – 15 NOV 2004
An envelop of 100 x 80 is to be cut from a single sheet with 8 mm width strip. Draw the development
20
30
A Rectangular box of 50 x 30 x 20
A CUBICAL BOX OF 25 mm IS CUT AT 45 DEG, THE BOTTOM FACE IS 10mm WIDE
A CUBICAL BOX OF 25 mm IS CUT AT 45 DEG, THE BOTTOM FACE IS 10mm WIDE
A PRISM 40 X 30 X 50 HIGH RESTING AT 45 DEG IS CUT BY A PLANE AT 45 DEG CUTTING THE AXIS AT 15 MM FROM TOP
A PRISM 40 X 30 X 50 HIGH RESTING AT 45 DEG IS CUT BY A PLANE AT 45 DEG CUTTING THE AXIS AT 15 MM FROM TOP
A PRISM 40 X 30 X 50 HIGH RESTING AT 45 DEG IS CUT BY A PLANE AT 45 DEG CUTTING THE AXIS AT 15 MM FROM TOP
A PRISM 40 X 30 X 50 HIGH RESTING AT 45 DEG IS CUT BY A PLANE AT 45 DEG CUTTING THE AXIS AT 15 MM FROM TOP
A PRISM 40 X 30 X 50 HIGH RESTING AT 45 DEG IS CUT BY A PLANE AT 45 DEG CUTTING THE AXIS AT 15 MM FROM TOP
A PRISM 40 X 30 X 50 HIGH RESTING AT 45 DEG IS CUT BY A PLANE AT 45 DEG CUTTING THE AXIS AT 15 MM FROM TOP
A PRISM 40 X 30 X 50 HIGH RESTING AT 45 DEG IS CUT BY A PLANE AT 45 DEG CUTTING THE AXIS AT 15 MM FROM TOP
21st NOV 2007
NOTE – BOTH ARE ‘A’ D A
C
A
B
C
D
A
E
F
G
H
E
B H E
G F
CUT EDGE AE
D A
C
C
D
A
B
C
G
H
E
F
G
B H E
G F
CUT EDGE CG
IF CUT EDGE IS CG WHAT WILL BE 1 TO 10 – TEACHER EXPLAINS D A
C
1
2
3
4
5
6
7
8
9
10
B H E
G F
1 –C, 6- ,
2-D, 7-
3-A, 8-
4-B, 9-
5-C 10
EXERCISE -1 D A
C
1
2
3
4
5
6
7
8
9
10
B H E
G F
IF CUT EDGE IS BF WHAT LETTERS SHALL BE AT 1 TO 10 – WRITE ANSWERS
ANS TO EX - 1 D A
C
1
2
3
4
5
6
7
8
9
10
B H E
G F
1-B 6-F
2-C 7-G
3-D 8-H
4-A 9-E
5-B 10-F
IF CUT EDGE IS BF - ANSWERS
TOP FACE CAN BE ATTACHED TO AB OR BC OR CD OR DA D
D A
C
AA
C BB C
D
A
F
H
E
B H E
G F
E
G
TOP FACE ATTACHED TO ‘AB’
TOP FACE CAN BE ATTACHED TO AB OR BC OR CD OR DA B
D A
C
A
A
B CC
DD
A
E
F
H
E
B H E
G F
G
TOP FACE ATTACHED TO ‘CD’
TOP FACE CAN BE ATTACHED TO AB OR BC OR CD OR DA A D D A
C
A
BB
C
D
A
E
F
G
H
E
B H E
G F
TOP FACE ATTACHED TO ‘BC’
D
D A
C
AA
C BB C
D
A
H
E
B H E
G F
E
FF
G
E
H
NOTE CC EE HH
TOP FACE CAN BE ATTACHED TO AB OR BC OR CD OR DA D
D A
C
AA
C BB C
D
A
F
H
E
B H E
G F
E
G
TOP FACE ATTACHED TO ‘AB’
EXERCISE - 2 D
11
A
C
12 3 4
1 2
5
B H E
G F
6
7
8 13
9 14
IF CUT EDGE IS BF WHAT LETTERS SHALL BE AT 1 TO 14 – WRITE ANSWERS
10
ANS TO EX - 2 D
11
A
C
12 3 4
1 2
5
B H E
G F
6
7
8 13
9
10
14
IF CUT EDGE IS BF 1-B 2-C 3-D 4-A 5-B 11-B 6-F 7-G 8-H 9-E 10-F 13-G
12-A 14-F
ANS TO EX - 2 D
11
A
C
12 3 4
1 2
5
B H E
G F
F
G
H G
E
F
F
IF CUT EDGE IS BF 1-B 2-C 3-D 4-A 5-B 11-B 6-F 7-G 8-H 9-E 10-F 13-G
12-A 14-F
EXERCISE - 3 A
F B
E D C
L G H
10
1
2
12
13
9
11 3 4
8 5
6
7
K J I
14 15 16
17 22
19
IF CUT EDGE IS BH WHAT LETTERS SHALL BE AT 1 TO 22 – WRITE ANSWERS
20 21
18
ANS TO EX - 3 A
F B
E D C
L G H
10
1
2
12
13
9
11 3 4
8 5
6
7
K J I
14 15 16
17
18
22
19 20 21
IF CUT EDGE IS BH 1-B 2-C 3-D 4-E 5-F 6-A 7-B 8-A 9-B 10-C 11- D 12-H 13-I 14-J 15-K 16-L 17-G 18-H 22-H 21-I 20-J 19--K
EXERCISE - 4 1
7
C 4
A
6
5 3
2
4
B
F D
E
6
8
7
IF CUT EDGE IS AD WHAT LETTERS AT 1 TO 10 – WRITE ANSWERS
10
9
ANS TO EX - 4 1
7
C 4
A
6
5 3
2
4
B
F D
E
6
8
7
IF CUT EDGE IS AD 1-A 2-B 3-C 4-A 5-A 6-D 7-E 8-F 9-D 10-D
10
9
EXERCISE - 5 A
7
C 4
A
6
5 2
3
4
B
F D
E
D
7
8
9
WHAT IS THE CUT EDGE 10 WHAT IS LENGTH AB, BC, CD, DE, EF, FD
ANS TO EXERCISE - 5 A
7
C 4
A
6
5 3
2
4
B
F D
E
D
8
7 10
WHAT IS THE CUT EDGE AD AB-6, BC-7, CA-4, DE-6, EF-7, FD-4
9
IMAGINARY SURFACE LINES ARE CALLED SURFACE GENERATORS – GENERALLY 8 OR 12 SURFACE GENERATORS
PYRAMIDS
FACE EDGES TAPER TO A POINT
PRISMS
FACE EDGES VERTICAL
PYRAMIDS
FACE EDGES TAPER TO A POINT
O O
A B(C)
A(D) D A
O
C B
D
B C
O O
B(C)
D A
O
A
C B
D
A
B
A(D)
C
PRISMS
FACE EDGES VERTICAL
A(D)
B(C) D
A
B
C
D A
D
C B H
E(H) D(H) A(E)
E F(G) H C(G) B(F)
CUT EDGE DH
E
F
G
H
G F
D A(D)
B(C) D A
C B C
D A
D
C B H
E(H) D(H) A(E)
E F(G) H E C(G) H B(F)
CUT EDGE DH
F G G
H
G F
D
ΠD
ΠD/8 IMAGINARY SURFACE LINES ARE CALLED SURFACE GENERATORS – GENERALLY 8 OR 12 SURFACE GENERATORS
Exercise – 6 Draw the development of the surfaces of a rectangular prism of length 4 cm, width 3 cm, height 8 cm
DRAW VIEW FROM TOP (PLAN VIEW ), VIEW FROMFRONT(ELEVATION), TRANSFER WIDTHS FROM PLAN, HEIGHTS FROM ELEVATION A’(D’)
B’(C’) A
B
C
D
A
E’(H’) D(H)
F’(G’) E
F
G
H
E
A(E)
C(G)
B(F)
Exercise – 7 Draw the development of the surfaces of a pentagonal prism of side 3 cm, height 8 cm
DRAW VIEW FROM TOP (PLAN VIEW ), VIEW FROMFRONT(ELEVATION), TRANSFER WIDTHS FROM PLAN, HEIGHTS FROM ELEVATION
Exercise – 8 Draw the development of the surfaces of a triangular prism of side 3 cm, 4 cm , and 6 cm and height 8 cm
DRAW VIEW FROM TOP (PLAN VIEW ), VIEW FROMFRONT(ELEVATION), TRANSFER WIDTHS FROM PLAN, HEIGHTS FROM ELEVATION
Exercise – 9 Draw the development of the surfaces of a cylinder of radius 3.5 cm, and height 9 cm
TRANSFER THE WIDTHS WITH A PROTRACTOR OR BY CALCULATION. CIRCUMFERANCE= 2*PI*R =2*22/7* 3.5 = 22 CM. DIVIDE BY 8 = 2.75 CM
PYRAMIDS
FACE EDGES TAPER TO A POINT
IN PYRAMIDS EDGES WILL BE INCLINED TO BOTH THE PLANES, VP AND HP. THE STANDARD PROCEDURE TO GET TRUE LENGTH IS TO ROTATE THE LINES, AROUND VERTICAL AXIS WITH TOP POINT FIXED. THE BOTTOM POINT WILL REMAIN IN THE SAME HEIGHT AND HENCE THE LOCUS WILL BE PARALLEL TO XY LINE IN VP. IN HP WHEN LINE IS ROTATED PARALLEL TO XY, IT IS PARALLEL TO VP AND WILL SHOW REAL LENGTH
o b’ X
b
a’
a
o
Y
LINE OA IS INCLINED BOTH TO VP AND TO HP IN BOTH VIEWS, HENCE WILL NOT GIVE TRUE LENGTH O
O
B(C)
A(D) D A
O
A
C B
D
A B
C
TO GET TRUE LENGTH OF OA, ROTATE IN PLAN VIEW, SO THAT IT BECOMES PARALLEL TO VP O
O
B(C)
A(D) D A
O
A
C B
D
A B
C
AB, BC, CD, DA ARE LYING IN HP, HENCE ARE PARALLEL TO HP, AND HAVE TRUE LENGTHS IN VIEW FROM TOP O
O
B(C)
A(D) D A
O
A
C B
D
A B
C
Exercise – 10 Draw the development of the surfaces of a pyramid of base 8cm wide, 6 cm depth and height 9 cm
AB, BC, CD, DA ARE LYING IN HP, HENCE ARE PARALLEL TO HP, AND HAVE TRUE LENGTHS IN VIEW FROM TOP O
O
B(C)
A(D) D A
O
A
C B
D
A B
C
DEVELOPMENT OF CUT SURFACES DR. R. VASUDEVAN DIRECTOR / SET 12 – 15 NOV 2004
An envelop of 100 x 80 is to be cut from a single sheet with 8 mm width strip. Draw the development
20
30
A Rectangular box of 50 x 30 x 20
A CUBICAL BOX OF 25 mm IS CUT AT 45 DEG, THE BOTTOM FACE IS 10mm WIDE
A CUBICAL BOX OF 25 mm IS CUT AT 45 DEG, THE BOTTOM FACE IS 10mm WIDE
A PRISM 40 X 30 X 50 HIGH RESTING AT 45 DEG IS CUT BY A PLANE AT 45 DEG CUTTING THE AXIS AT 15 MM FROM TOP
A PRISM 40 X 30 X 50 HIGH RESTING AT 45 DEG IS CUT BY A PLANE AT 45 DEG CUTTING THE AXIS AT 15 MM FROM TOP
A PRISM 40 X 30 X 50 HIGH RESTING AT 45 DEG IS CUT BY A PLANE AT 45 DEG CUTTING THE AXIS AT 15 MM FROM TOP
A PRISM 40 X 30 X 50 HIGH RESTING AT 45 DEG IS CUT BY A PLANE AT 45 DEG CUTTING THE AXIS AT 15 MM FROM TOP
A PRISM 40 X 30 X 50 HIGH RESTING AT 45 DEG IS CUT BY A PLANE AT 45 DEG CUTTING THE AXIS AT 15 MM FROM TOP
A PRISM 40 X 30 X 50 HIGH RESTING AT 45 DEG IS CUT BY A PLANE AT 45 DEG CUTTING THE AXIS AT 15 MM FROM TOP
A PRISM 40 X 30 X 50 HIGH RESTING AT 45 DEG IS CUT BY A PLANE AT 45 DEG CUTTING THE AXIS AT 15 MM FROM TOP
