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.
-
\(4(6 + 5\pi)\)
- \(4(6 + 2\pi)\)
- \(4(3 + 3\pi)\)
- \(4(3 + 5\pi)\)
The correct answer is: 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 = \(r\theta + 2r\)
= \(12 \times \frac{5\pi}{3} + 2(12) = 20\pi + 24\)
= \(4(5\pi + 6)\)