Page 69 - WCS - Electrical

Exercise 1.7.26
Workshop Calculation & Science - Electrician & Wireman
Mensuration - Area and perimeter of circle, semi-circle, circular ring, sector
of circle, hexagon and ellipse
Circle

r
= 196
It is the path of a point which is always equal from its
= 14 m
centre is called a circle.
r = radius of the circle
Circumference
= 2πr unit
d = diameter of the circle
22
22
x 14
= 2 x
7
π =
= 3.14
7
= 88 m
Area of the circle = πr
2
wire is in the form of a circle of radius 49 cm.
radius of circle r
= 49 cm
side of square
= ?
Perimeter of the square = Perimeter of the circle
4a
= 2πr
22
π
4a
x 49
= 2 x

d unit
(or)
=
7
2
2
4
4a
= 308
Circumference of the circle 2πr (or) πd unit
Examples
308
=
a
1 Find the area of a circle whose radius is 1.54 m. Also
4
find its circumference.
= 77 cm
= 1.54 cm
radius r
4 Find its radius if the difference between the
Area A
= ?
circumference and diameter of a circle is 28 cm.
= ?
Circumference C
Circumference - Diameter = 28 cm
= πr unit
A
2
2πr - d = 28
22
x 1.54 x 1.54
=
2πr - 2r = 28
7
2r (π - 1)= 28
= 7.4536 m
2
C
= 2πr unit
22
2r (
- 1) = 28
22
7
= 2 x
7
22
-
7
= 9.68 m 2 x 1.54 3 Find the side of square into which it can be bent if a
2r ( ) = 28
2 Find out the circumference if the area of a circular shape 7
of land is 616 m . WORKSHOP CALCULATION & SCIENCE - CITS
2
A = πr unit 2 2r x 15 = 28
2

616 7
r 2 =
π 28x7
r =
616x7 15x2
=
22 = 6.53 cm
= 196 5 What is the side of the largest square cut out from a
5 What is the side of the largest square cut out from a circle of 50 cm dia.? 1 2
64 circle of 50 cm dia.? = x 50 x 16 cm
2
5 What is the side of the largest square cut out from a 1
Diagonal of a square = Diameter of the circle = 400 cm 2 2
circle of 50 cm dia.? = x 50 x 16 cm
2
2a
= 50
2
Diagonal of a square = Diameter of the circle = 400 cm 2
r π
Area of Semi circle = unit 2
2
2a = 50 50 r π 2
a = Area of Semi circle = 2 unit 2 1
2
50 = π x 15 2 x cm 2
a = 50 2
1
2
π
15
x
x cm
= 2 = = 353.57 cm 2 2 2
1.414
50 Total area of the figure= 500 + 400 + 353.57
=
= 35.36 cm = 353.57 cm 2
1.414 = 1253.57 cm 2
Total area of the figure= 500 + 400 + 353.57
6 Calculate the area of the figure given below.
= 35.36 cm
6 Calculate the area of the figure given below. 7 Find the area of remaining steel plate if in a rectangular
= 1253.57 cm
2
6 Calculate the area of the figure given below. steel plate 16 cm x 12 cm, there are 6 holes each 4
cm in diameter.
7 Find the area of remaining steel plate if in a rectangular
steel plate 16 cm x 12 cm, there are 6 holes each 4
Area of a rectangular plate = length x breadth unit 2
cm in diameter.
= 16 x 12
Area of a rectangular plate = length x breadth unit 2
= 192 cm 2
= 16 x 12
No. of holes = 6
= 192 cm 2
Radius of hole = 2 cm
= 6
No. of holes
Area of rectangle = lb unit 2 Area of 6 holes = 6 x πr unit 2
2
= 25 x 20 cm 2 Radius of hole = 2 cm
Area of rectangle = lb unit 2 Area of 6 holes = 6 x πr unit 2
22
2
= 500 cm 2 = 6 x x 2 x 2 unit 2
= 25 x 20 cm 2 7
1 2 22 2
= 500 cm
Area of Trapezium = x (a + b) h = 6 x x 2 x 2 unit
= 75.43 cm
2
2 7
1 Area of remaining plate = 192 - 75.43
1
Area of Trapezium = x (a + b) h = 75.43 cm 2
2 = x (30 + 20) 16 cm 2
= 116.57 cm
2
2 Area of remaining plate = 192 - 75.43
1
= x (30 + 20) 16 cm 2 = 116.57 cm 2
2
5 What is the side of the largest square cut out from a Semi circle 1
circle of 50 cm dia.? = x 50 x 16 cm 2 Examples
2
A semi circle is a sector whose central angle is 180º.
Semi circle
Diagonal of a square = Diameter of the circle Length of arc of semi circle. 2 1 Calculate the circumference and area of a semi circle
= 400 cm
Examples
A semi circle is a sector whose central angle is 180º. whose radius is 6 cm.
180
2a = 50 Length of arc of semi circle. r π 2 unit 2 1 Calculate the circumference and area of a semi circle
= 6 cm
radius r
=
Length of arc  = 2πr x
Area of Semi circle
whose radius is 6 cm.
360
50 180 2 Area A = ?
a = Length of arc  = 2πr x 1 radius r = 6 cm
360
2 = 2πr x = πr unit 1 2 Circumference c = ?
2
π
x
15
= ?
Area A
=
x cm
2
1
50 = 2πr x = πr unit 2 Circumference c = ? r π 2 unit 2
A
=
r π
2
= Area of semi circle = 2 = 353.57 cm 2 2
Sq. units
1.414 2 r π 2
2
Total area of the figure= 500 + 400 + 353.57 A = 22 unit 2
r π
= 35.36 cm Area of semi circle = Sq. units 2 1 2
2 = 1253.57 cm 2 = 7 x x 6
2
1
6 Calculate the area of the figure given below. = 22 x x 6 2
7 Find the area of remaining steel plate if in a rectangular 22 2 1
7
steel plate 16 cm x 12 cm, there are 6 holes each 4 Area (A) = 7 x x 36
2
cm in diameter. 56 22 1
2
2πr
7
CITS : WCS - Electrical - Exercise 5
Area of a rectangular plate = length x breadth unit 2 Area (A) = 396 x x 36
Perimeter of a semi circle = + 2r = 7 = 56.57 cm 2
2
= 16 x 12 396
2πr
= πr + 2r
22
Perimeter of a semi circle = 2 2 + 2r = 7 = 56.57 cm 2
= 192 cm

7
= 6
No. of holes = r (π + 2) unit Perimeter of a semicircle = 6( 22 x 2)
= πr + 2r
WCS - Electrician & Wireman : (NSQF - Revised 2022) - 1 Year : Exercise 1.7.26
st
Radius of hole = 2 cm Perimeter of a semicircle = 6( 7 x 2) 65
= r (π + 2) unit
Area of rectangle = lb unit 2 Area of 6 holes = 6 x πr unit 2 st 65
2
WCS - Electrician & Wireman : (NSQF - Revised 2022) - 1 Year : Exercise 1.7.26
= 25 x 20 cm 2
22
= 500 cm 2 = 6 x x 2 x 2 unit 2
7
1
Area of Trapezium = x (a + b) h = 75.43 cm 2
2
Area of remaining plate = 192 - 75.43
1
= x (30 + 20) 16 cm 2
2 = 116.57 cm 2
Semi circle
Examples
A semi circle is a sector whose central angle is 180º.
Length of arc of semi circle. 1 Calculate the circumference and area of a semi circle
whose radius is 6 cm.
180
Length of arc  = 2πr x radius r = 6 cm
360
Area A = ?
1
= 2πr x = πr unit Circumference c = ?
2
r π 2
r π 2 A = unit 2
Area of semi circle = Sq. units 2
2
22 1
= x x 6 2
7 2
22 1
Area (A) = x x 36
7 2
2πr 396
Perimeter of a semi circle = + 2r = = 56.57 cm 2
2 7
= πr + 2r 22
= r (π + 2) unit Perimeter of a semicircle = 6( 7 x 2)
WCS - Electrician & Wireman : (NSQF - Revised 2022) - 1 Year : Exercise 1.7.26 65
st