Page 68 - WCS - Electrical
P. 68

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
                                        centre is called a circle.
                                                                                                                   = 14 m
                                                       r = radius of the circle
                                                                                                   Circumference
                                                                                                                   = 2πr unit
                                                       d = diameter of the circle
                                                                                                                         22
                                                           22
                                                                                                                             x 14
                                                                                                                   = 2 x
                                                       π =
                                                              = 3.14
                                                                                                                         7
                                                            7
                                                                                                                   = 88 m
                                        Area of the circle = πr
                                                            2
                                                                                              3 Find the side of square into which it can be bent if a
                                                                                                 wire is in the form of a circle of radius 49 cm.
                                                                                                                   = 49 cm
                                                                                                   radius of circle r
                                                                                                   side of square
                                                                                                                   = ?
                                                                                                 Perimeter of the square = Perimeter of the circle
                                                                                                     4a
                                                                                                            = 2πr
                                                                                                                  22
                                                         π
                                                                                                            = 2 x
                                                                                                                      x 49
                                                                                                     4a

                                                (or)
                                                                                                                  7
                                                           d unit
                                                        =
                                                             2
                                                                 2
                                                         4
                                                                                                            = 308
                                                                                                     4a
                                        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
                                              radius r
                                                              = 1.54 cm
                                                                                              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
                                                       A
                                                              = πr  unit
                                                                      2
                                                                  2
                                                                                                                   2πr - d = 28
                                                                 22
                                                                    x 1.54 x 1.54
                                                              =
                                                                                                                   2πr - 2r = 28
                                                                 7
                                                                                                                       2r (π - 1)= 28
                                                              = 7.4536 m
                                                                        2
                                                              = 2πr unit
                                                       C
                                                                                                                   2r (
                                                                    22
                                                                                                                    7
                                                              = 2 x
                                                                       x 1.54
                                                                    7
                                                                                                                       7
                                                                                                                    22
                                                              = 9.68 m
                                                                                                                   2r (  22    -  - 1) = 28
                                                                                                                         ) = 28
                                        2 Find out the circumference if the area of a circular shape                 7
                                           of land is 616 m .
                                                         2
                                                     WORKSHOP CALCULATION & SCIENCE - CITS                         2r x   15  = 28
                                                              = πr  unit
                                                            A
                                                                  2
                                                                      2

                                                                 616                                                 7
                                                              =
                                                          r
                                                          2


 Workshop Calculation & Science - Electrician & Wireman          π  Exercise 1.7.26                                          28x7
 Workshop Calculation & Science - Electrician & Wireman             Exercise 1.7.26                                    r   =
                                                                 616x7
 Workshop Calculation & Science - Electrician & Wireman      Exercise 1.7.26                                                 15x2
 Mensuration - Area and perimeter of circle, semi-circle, circular ring, sector
                                                              =
 Mensuration - Area and perimeter of circle, semi-circle, circular ring, sector
                                                                  22
 of circle, hexagon and ellipse
 Mensuration - Area and perimeter of circle, semi-circle, circular ring, sector                                            = 6.53 cm
 of circle, hexagon and ellipse
 of circle, hexagon and ellipse                               = 196
 Circle

 Circle                                  64            r      =  196

 Circle  It is the path of a point which is always equal from its  r  =  196

 centre is called a circle.
 It is the path of a point which is always equal from its  r  =  196  = 14 m
 It is the path of a point which is always equal from its     = 14 m
 centre is called a circle.
 centre is called a circle.  r = radius of the circle  Circumference  = 2πr unit
                                                       = 14 m
  r = radius of the circle                    Circumference   = 2πr unit
  d = diameter of the circle
 r = radius of the circle              Circumference   = 2πr unit
  d = diameter of the circle                                        22
      22
                                                              = 2 x
 d = diameter of the circle                                  22 = 2 x   22   x 14
         = 3.14
                                                                    7
  π =
      22
  22 π =   7  = 3.14                                   = 2 x    x 14 7   x 14
 π =   = 3.14 7                                              7= 88 m
 Area of the circle = πr 2                                    = 88 m
 7
 Area of the circle = πr 2              3 Find the side of square into which it can be bent if a
                                                       = 88 m
 Area of the circle = πr 2  3  Find the side of square into which it can be bent if a wire is in the form of a circle of radius 49 cm.
                                        3 Find the side of square into which it can be bent if a
                                           wire is in the form of a circle of radius 49 cm.
                                 3 Find the side of square into which it can be bent if a
                                           wire is in the form of a circle of radius 49 cm.
                                              radius of circle r
                                                              = 49 cm
                                    wire is in the form of a circle of radius 49 cm.
                                              radius of circle r  = 49 cm
                                              side of square
                                       radius of circle r  = 49 cm = ?
                                                              = ?
                                              side of square
                                           Perimeter of the square = Perimeter of the circle
                                       side of square  = ?
                                           Perimeter of the square = Perimeter of the circle
                                                       = 2πr
                                                4a
                                    Perimeter of the square = Perimeter of the circle
                                                4a     = 2πr
                                        4a      = 2πr        22
    π                                           4a     = 2 x   22   x 49

 (or)   =  π d unit 2                           4a    22 = 2 x   7   x 49
       2
 (or) π   =  4   d unit 2               4a      = 2 x    x 49 7
       2
 (or)   =  4   d unit 2 4                       4a    7= 308
 2
 Circumference of the circle 2πr (or) πd unit
 Circumference of the circle 2πr (or) πd unit   4a     = 308
 Examples
 Circumference of the circle 2πr (or) πd unit  4a  = 308   308
 Examples                                        a     =   308
 1 Find the area of a circle whose radius is 1.54 m.  Also
 Examples                                        a  308 =   4
 find its circumference.
 1 Find the area of a circle whose radius is 1.54 m.  Also   a  =   4
 1 Find the area of a circle whose radius is 1.54 m.  Also  4  = 77 cm
 find its circumference.
 radius r
 find its circumference.  = 1.54 cm                    = 77 cm
 radius r  = 1.54 cm                    4 Find its radius if the difference between the
                                                = 77 cm
         = ?
 radius r  Area A  = 1.54 cm            4 Find its radius if the difference between the
                                           circumference and diameter of a circle is 28 cm.
         = ?
 Area A
 Circumference C
                                 4 Find its radius if the difference between the
                                           circumference and diameter of a circle is 28 cm.
 Area A  = ?  = ? 4  Find its radius if the difference between the circumference and diameter of a circle is 28 cm.
                                              Circumference - Diameter = 28 cm
 Circumference C  = ?               circumference and diameter of a circle is 28 cm.
  A
            2
 Circumference C  = ?  = πr  unit 2           Circumference - Diameter = 28 cm
                                                              2πr - d = 28
  A      = πr  unit 2                  Circumference - Diameter = 28 cm
            2
         2  22
 A  = πr  unit =   22   x 1.54 x 1.54                         2πr - d = 28
     2
                                                              2πr - 2r = 28
    22   =   7   x 1.54 x 1.54                         2πr - d = 28
                                                              2πr - 2r = 28
           7
  =     x 1.54 x 1.542                                            2r (π - 1)= 28
                                                       2πr - 2r = 28
         = 7.4536 m
    7    = 7.4536 m 2                                             2r (π - 1)= 28
  C
         = 2πr unit
  = 7.4536 m 2                                             2r (π - 1)= 28
                                                               22
  C      = 2πr unit                                           2r (  22   - 1) = 28
               22
 C  = 2πr unit   22   x 1.54                            22     7   - 1) = 28
                                                              2r (
         = 2 x
                                                               7
        22 = 2 x   7   x 1.54                          2r (   - 1) = 28
           x 1.54 7
  = 2 x   = 9.68 m                                      7      22 - 7
        7                                                     2r (  22 - 7  ) = 28
         = 9.68 m

                                                           7
 2 Find out the circumference if the area of a circular shape   22 - 2r (  7  ) = 28
  = 9.68 m
 of land is 616 m .
 2 Find out the circumference if the area of a circular shape         2r (  ) = 28 7
    2
 2 Find out the circumference if the area of a circular shape  7   15
 of land is 616 m .
    2
       A
         = πr  unit
                 2

             2
 of land is 616 m .       A  = πr  unit 2                     2r x   15  = 28
 2
                                                                7

             2
                                                         15
      A  = πr  unit 2 616                              2r x         2r x  = 28  = 28

     2
                                                                7
         =
     r
    2

            616
    616 =
        r 2  π                                           7              28x7
       r 2  =   π                                                 r  =   28x7
     π      616x7                                                 r    15x2
                                                                 28x7 =
         =   616x7                                         r  =        15x2
    616x7 =   22                                                15x2 = 6.53 cm
             22
  =      = 196                                                       = 6.53 cm
     22                                                    55 = 6.53 cm
 64  = 196  = 196                           CITS : WCS - Electrical - Exercise 5
 64
 64
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