Page 70 - WCS - Electrical
P. 70

5 What is the side of the largest square cut out from a
                                                                1
                                                5 What is the side of the largest square cut out from a
                                                                                                                            1
                                                              =   x 50 x 16 cm
 circle of 50 cm dia.?
                                                                                                                          =   x 50 x 16 cm
                                                  circle of 50 cm dia.?
                                        5 What is the side of the largest square cut out from a
                                                                                                                            2
                                                                                                                    1
 Diagonal of a square = Diameter of the circle
                                                              = 400 cm
                                                                       2
                                          circle of 50 cm dia.?
                                                                                                                                  2
                                                  Diagonal of a square = Diameter of the circle
                                                                                                                          = 400 cm
                                                                                                                    2
   2a
         = 50
                                                                   2
                                                                  r π
                                          Diagonal of a square = Diameter of the circle
                                                                                                                  = 400 cm
                                                                                                                           2
                                                                     unit
                                            Area of Semi circle
                                                              =   2a
                                                                        2
                                                                                                                              r π
                                                                                                                               2
                                                                                                                                 unit
                                                                                                                          =
                                                                                                        Area of Semi circle
                                                                  2
                                                                                                                              2
            50
                                                                                                                       2
                                                                                                                      r π
                                                                                                                  =
                                                                                                                         unit
  a
         =
                                                                        50
                                                                                                                            2
                                                                         1
                                                              a
                                                                      2 =
                                                                                                                      2
             2
                                                                π
                                                                       x   cm
                                                              =
                                                                50
                                                                                                                                  2
                                                                                                                               15
                                                                                                                            π
                                                                                                                               x
                                                                                                                          =
                                                                                                                                   x   cm
                                                             =
                                                      a 2a   = 50 2  x  15 = 50 2 2  2 2        Area of Semi circle  =   x 50 x 16 cm 2  2 1  2 2
             50                                                                                                           2  1       2
                                                                 2

         =                                                    = 353.57 cm 50                                      =  π  x  15   x   cm 2
                                                                         2
                                                                                                                             2
                                                                     =
           1.414                                     WORKSHOP CALCULATION & SCIENCE - CITS                                = 353.57 cm 2
                                                                       1.414
                                                                 50
                                            Total area of the figure= 500 + 400 + 353.57
                                                                                                                  = 353.57 cm
                                                                                                                             2
         = 35.36 cm                                          =                                          Total area of the figure= 500 + 400 + 353.57
                                                               1.414 = 35.36 cm
                                                              = 1253.57 cm 2                                                           2
                                                                                                                          = 1253.57 cm

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

         =   x (30 + 20) 16 cm 2            Perimeter of a semicircle = 6(    = πr + 2r                 Perimeter of a semicircle = 6(  22    x 2)
                                                                      7
           = r (π + 2) unit
                                                              = 116.57 cm
                                                                         2
           2
                                                                                                                                   7
                                                                = πr + 2r   = r (π + 2) unit
                                                                                                                          22
 WCS - Electrician & Wireman : (NSQF - Revised 2022) - 1  Year : Exercise 1.7.26      65        Perimeter of a semicircle = 6(  7    x 2)
                                                      st
                                                               = r (π + 2) unit
                                                             WCS - Electrician & Wireman : (NSQF - Revised 2022) - 1  Year : Exercise 1.7.26
                                                                                                                  st
 Semi circle                                         WCS - Electrician & Wireman : (NSQF - Revised 2022) - 1  Year : Exercise 1.7.26              65
                                                                                                          st
           Examples                      Examples                                                                                         65
 A semi circle is a sector whose central angle is 180º.
                                         1 Calculate the circumference and area of a semi circle
 Length of arc of semi circle. 1  Calculate the circumference and area of a semi circle whose radius is 6 cm.
                                           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
                                                           57    22   1
                                                              =
                                                                    x    x 6
                                                                           2
                                            CITS : WCS - Electrical - Exercise 5
                                                                      2
                                                                 7
                                                                 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
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