Page 30 - CITS - WCS - Mechanical

WORKSHOP CALCULATION - CITS

Ellipse

Major axis AB = 2a 1
2
2 x S(S a)(S b)(S c) x b 2 x 15 x 3 x 7 x 5 144 2 2 x 15(15 2)(15 8)(15 10)
Half of Major axis OB = a, 4 60
Minor axis CD = 2b 40 180 a b c
2
20 area 500 1000 2 x S(S a)(S b)(S c) 60 4a b 2 2 x 1575
Half of Minor axis OC = b 10 base 20 50 4 3 2
Area of ellipse A = x a x b unit² 3 1 15 x 2 60 x 2 6
2
30 12 8 10 S b 2 3 P x bh Base 2 Height 2 2 S b 2 5 3 2
2
2
2
2 (a b2 2 ) 4 2 2 3.5 10
+
Perimeter of ellipse P = 2π unit
2
unit
2 1 b 2 2 4 x 5 6 2 3 9 10 12 31 S(S a)(S b)(S c) 15.5 x 6.5 x 5.5 x 3.5
2
b
4a
9
16
25
2
1
2
1 Find its area and perimeter, if the major and minor axis of an ellipse are 12 cm and 8 cm respectively 2)(15 8)(15 10)
4
4
2
2
x
2
S(S
x
2
a)(S
15
x
2
x
3
x
5
x
7
b)(S
x
c)
b
144
15(15
60
Solution: 4 θ 2 2
15.5(15.5 9)(15.5 10)(15.5 3.5) 1939.4375 40 274.91 Length of arc l x2 r unit a b c (a b )
+
180
2
area
Major axis 2a 20 = 12 cm 500 1000 2 x S(S a)(S b)(S c) 3 60 4a b 2 360 1575 x2 2 2 unit
base
10 12 22 20 50 2 2 4 22 22 2
22
(6
2 x
26 2 x

x
5.1

cm
a 30 = = 6 cm 6 x 2 4 cm 2 2 2 3 22 P 2 3 4 ) 1 unit 2 Base 2 (36 16) unit 15 7 x 2 60 2 x 6 7 x S b 32.06 5 3 2
2
2
2
bh
12
8

x

10
2
7
2 Height
2
7
7

b
S
2
2
Minor axis 2b 2 = 8 cm 4 2 2 3.5 10
1 1 3 9 10 12 31
2
2
2 x S(S a)(S b)(S c) x b 2 x 15 x 3 x 7 x 5 144 60 2 2 x 15(15 2)(15 8)(15 10) 1 b 2 2 4 x 5 6 2 S(S a)(S b)(S c) 15.5 x 6.5 x 5.5 x 3.5
25
8 16
2
2
2
x
c)
b
4 b 2 x S(S a)(S b)(S 9 = = 4 cm 4 2 x 4a 3 b x 7 x 5 144 60 2 4 2 x 15(15 2)(15 8)(15 10)
15
x
4
b
2 a
c
2
20 area 500 1000 2 x S(S a)(S b)(S c) 40 180 60 4a b 2 2 x 15.5(15.5 9)(15.5 10)(15.5 3.5) 40 1939.4375 274.91 2 2 θ a b r (a b 2 )
1575
2
180
c
+
1000
x2
3
1575
x
4a
b
2 S(Sx
2
a)(S

Area A
= π x a x b unit²
10 base 20 50 2 x 4 a)(S b)(S 20 1 area 500 15 x 3 x 7 x 5 144 60 b)(S 2 c) 15(15 2)(15 60 10) Length 2 of arc l 360 2 unit 2 2 unit
2
2
3
c)
S(S
x
x
4
b
8)(15
x
2
15
3 1 10 x 4 base 2 20 6 50
x
2 60
30 12 8 10 S b 2 3 P x bh Base 2 Height 2 2 12 S 2 22 b 2 x 340 2 3 180 22 1 (6 4 2 ) 2 22 2 (36 15 16) 2 x a b 60 c x 2 22 6 2 2 22
2
2
2
3
2
5
2
cm
30
x
bh

unit
Base
1000
2 60
2

3
b
5
4a
2
4
2 2 2 x S(S a)(S 2 b)(S 20 1 area 500 15 x 3 3.5 12 5 10 10 8 144 260 = 2 2 b x 6 4 4 4 P 2)(15 28)(15 2 10) 2 unit Height 2 2 2 x 1575 2 3.5 2 10 2 7 2 x 26 S 2 b x 7 x 2 5.1 2 32.06 cm
a)(S
S
2
x
S(S
b)(S
c) 15(15 x
7 2
c)
b
x
7
2
x
x
x
7
7
2 3

10
1 2 2 3 10 9 4 base 1220 31 50 2 2 = 75.43 cm² 6.5 x 15.5 x 5.5 x 3.5

c)
2
40
1 3
25 9 16 b 4a b 2 4 x 5 6 2 2 S(S a)(S b)(S 180 1 2 2 2 3 15 x a 2 60c b 9 10 x 2 12 6 31 15.5 x 6.5 x 5.5 x 3.5
area
1000
20
S(S
2
2
x
2

4 2 x S(S a)(S b)(S c) 500 1 x b 4 30 2 x 12 2 15 x 8 3 S(S 7 x 5 S 144 60 P x b 15(1 60 b Base b4a 4 2 2 5 x2 6 2 1575 2 2 S b 2 a)(S b)(S c)
3 2
bh
x
b)(S
x
9 c)
22
10 a)(S
2
2
Height
25
16
2

x
2
10)
8)(15
4a 2)(155
3
4
5
3
b
10 base 20 4 50 2 2 4 4 4 2 2 3.5 2 10 2
2
15.5(15.5 9)(15.5 10)(15.5 3.5) 1939.4375 274.91 Length of arc l 180 θ x2 r unit (a b 2 ) 6 b θ 2 2
+
3 40
1
10
3.5) 9 60

10)(15.5
2 2 2
+
1939.4375
274.91
2
20 area 30 12 1000 10 x2 S(S a)(S 3 P c) 1 b Perimeter (P) 9)(15.515.5(15.5 4 5 6 = 2 3 x 15 x 2 2 1575 unit 12 2 x a 31 c S b 2 a)(S 35 b)(S of c) arc l 15.5 x x2 r 5.5 x 3.5 (a b ) unit
500
360 60
2
unit
Length

2
2

bh
2

x Height b4a
x
8
b)(S
x
6.5
2
2
2
2 Base
2
2
2
S(S
2
10 base 2 20 50 S 25 b 9 16 4 2 4 4a b 3 4 3.5 2 10 2 2 2 360 2
4
12 22 22 (6 4 22 ) 22 (36 16) 22 22
2
3
2
x 6 x 4 cm 2 2 unit 1 3 2 3 1 unit 2 x 12 26 22 x 9 x 10 5.112 x 15 2 32.06 x 60 22 cm 6 2 4 2 22 (36 θ 22 2 22 2
2
31
16)
(6
(a
2
10)(15.5
2

9)(15.5
x
6.5
P
5.1
2 7 30 12 8 7 10 9 S 2 16 b 2 b 7 15.5(15.5 x bh 4 x 5 Base 2 2 Height 3.5) x 2 6 7 4 x 1939.4375 274.91 a)(SS S ) 2 Length c)b)(S 2 of 2 arc l 3 2 15.5 x unit r 5.5 x x 3.5 26 2 + b ) x unit 32.06 cm
cm

x
x2
2
unit b
S(
2 2
2 unit

2
=
7 6
2
2

2 5
b
2
25
4a
2
2 10
2 2 4 4 2 2 4 7 2 3.5 7 2 7 2 360 7 2 7

10
9
31
θ
1
2
2
2
12
15.5
22
274.91
15.5(15.5 9)(15.5 10)(15.5 22 3.5) 3 1939.4375 12 (6 4 2 ) S(S 22 (36 16) r 226.5 x x 5.5 (a 3.5 x 2 + 22 )b 2
arc l
c)
2
of
x2
2

25 9 16 b 4a b 4 x 5 6 x 6 x 4 cm 2 2 2 2 Length a)(S b)(S unit unit x 2 2 x x unit 32.06 cm
2

26
5.1
2

= unit
4 2 7 4 7 2 7 2 360 7 2 7
2
12
(36
2
10)(15.5
(6
15.5(15.5 9)(15.5 22 3.5) 2 22 1939.4375 4 2 ) 274.91 22 Length of 16) θ 22 x2 r unit 22 (a b 2 )
+
arc l

x
cm
x 6 x 4 cm 2 unit 2 = unit 2 x 26 2 2 x 5.1 32.06 unit
2 7 7 2 7 2 360 7 7 2
12 22 22 (6 4 2 ) 22 (36 16) 22 22
2
x 6 x 4 cm 2 2 unit 2 unit 2 x = 2 x x 5.1 32.06 cm
26
2 7 7 2 7 2 7 7
17
CITS : WCS - Mechanical - Exercise 5 CITS : WCS - Mechanical - Exercise 5