The perimeter of a sector of a circle of radius 21cm is 64cm. Find the angle of the sector [Take (pi = frac{22}{7})]
-
A.
70o -
B.
60o -
C.
55o -
D.
42o
Correct Answer: Option B
Explanation
Perimeter of a sector
= 2r + (frac{theta}{360^o}) x 2 x (frac{22}{7}) x 21
64 = 2 x 21 + (frac{theta}{360^o}) x 2 x (frac{22}{7}) x 21
64 = 42 + (frac{theta}{360^o}) x 44 x 3
64 – 42 = (frac{theta}{360^o}) x 11 x 3
22 = (frac{33theta}{90})
(theta = frac{22 times 30}{11})
= 60o