The angle subtended by an arc of a circle at the centre is (frac{pi}{3} radians). If the radius of the circle is 12cm, calculate the perimeter of the major arc.
-
A.
(4(6 + 5pi)) -
B.
(4(6 + 2pi)) -
C.
(4(3 + 3pi)) -
D.
(4(3 + 5pi))
Correct Answer: Option A
Explanation
The angle subtended by the minor arc = (frac{pi}{3} radians)
The angle subtended by the major arc = (2pi – frac{pi}{3} = frac{5pi}{3})
Perimeter of the major arc = (rtheta + 2r)
= (12 times frac{5pi}{3} + 2(12) = 20pi + 24)
= (4(5pi + 6))