SOLUTION: A sector of a circle of radius 6 cm subtends an angle of 105° at the centre. Calculate the: (i) perimeter; (ii) area; of the sector. [Take π = 22/7]

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Question 1210337: A sector of a circle of radius 6 cm subtends an angle of 105° at the centre. Calculate the:
(i) perimeter;
(ii) area;
of the sector.
[Take π = 22/7]
Answer by ikleyn(52754) About Me  (Show Source):
You can put this solution on YOUR website!
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A sector of a circle of radius 6 cm subtends an angle of 105° at the centre. Calculate the:
(i) perimeter;
(ii) area;
of the sector.
[Take π = 22/7]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

(i)   The perimeter of this sector is the sum of the arc length plus twice the length of the radius.

      The arc length is the circle circumference multiplied by the ratio of angles  105%2F360 = 7%2F24.

      So, we write for the atc length


          2%2Api%2Ar%2A%28105%2F360%29 = 2%2A%2822%2F7%29%2A6%2A%287%2F24%29 = %282%2A22%2A6%2A7%29%2F%287%2A24%29 = %2811%2A3%29%29%2F3 = 33%2F3 = 11  cm.


      Then the perimeter of the sector is  11 + 2*6 = 23 cm. 




(ii)  The area of the sector is  105%2F360 = 7%2F24  part of the area of the circle

          area of the sector = pi%2Ar%5E2%2A%28105%2F360%29 = %2822%2F7%29%2A6%5E2%2A%287%2F24%29 = %2811%2A3%5E2%29%2F3 = 11*3 = 33 cm^2

      using the given approximation.

Solved.