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. \(4(6 + 5\pi)\) B. \(4(6 + 2\pi)\) C. \(4(3 + 3\pi)\) D. \(4(3 + 5\pi)\)
Correct Answer: A
Explanation
The angle subtended by the minor arc = \(\frac{\pi}{3} radians\) The angle subtended by the major arc = \(2\pi - \frac{\pi}{3} = \frac{5\pi}{3}\) Perimeter of the major arc = \(r\theta + 2r\) = \(12 \times \frac{5\pi}{3} + 2(12) = 20\pi + 24\) = \(4(5\pi + 6)\)
