Page 74 - WCS - Electrical
P. 74

WORKSHOP CALCULATION & SCIENCE - CITS





              θ = Angle of sector of circle
              l = Arc length
              r = radius

              Length of Arc l =   θ   x 2πr unit
                              360°
              Perimeter P = 2r + l unit
                      θ                       lr
              Area =      x πr² unit²     (or)    A =    unit²
                    360°                      2

           1  Find the perimeter and area of a sector of circle of radius 7 cm and its angle is 120°.

              Given:
                 Angle of sector of circle = 120°
                 Radius = 7 cm
              To find:

                 Perimeter = ? , Area = ?
              Solution:

                 Length of arc (l)   =   θ   x 2πr unit
                                    360°
                                     120      22
                                  =      x 2 x    x 7 cm
                                     360      7
                                  = 14.67 cm
                 Perimeter        = 2r +l unit

                                  = 2 x 7 + 14.67 cm
                                  = 28.67 cm
                 Area             =   θ   x πr² unit²
                                    360°
                                    120°  22
                 Area             =      x    x 7 cm² = 51.33 cm²
                                    360°   7

           2  Find the radius of the circle if the angle is 60° and the area of a sector of a circle is 144 cm²,

              Given:

                 Area of sector of circle (A)   = 144 cm²
                 Angle of sector of circle θ   = 60°

              To find:
                 Radius of circle   = ?

              Solution:
                                      θ
                 Area (A)          =     x πr² unit²
                                    360°








                                                           61

                                            CITS : WCS - Electrical - Exercise 5
   69   70   71   72   73   74   75   76   77   78   79