An arc of a circle of radius \(2 \mathrm{~cm}\) subtends an angle of \(60^{\circ}\) at the centre. Find the area of the sector in term of \(\pi\)
A. \(\pi \mathrm{cm}^2\)
B. \(\frac{\pi}{6} \mathrm{~cm}^2\)
C. \(\frac{2 \pi}{3} \mathrm{~cm}^2\)
D. \(\frac{\pi}{3} \mathrm{~cm}^2\)
Correct Answer: C
Explanation
Area of sector \(=\frac{\theta}{360^{\circ}} \times \pi r^2\)
\begin{array}{l}
=\frac{60^{\circ}}{360^{\circ}} \times \pi \times(2 \mathrm{~cm})^2 \\
=\frac{1}{6} \times \pi \times 4 \mathrm{~cm}^2 \\
=\frac{2 \pi}{3} \mathrm{~cm}^2
\end{array}