Question

What is the area of a sector with a central angle of 4pi/3 radians and a radius of 11cm

Answer 1

$\bf \textit{area of a sector of a circle}\\\\ A=\cfrac{\theta r^2}{2}\quad \begin{cases} r=radius\\ \theta =angle~in\\ \qquad radians\\ ------\\ r=11\\ \theta =\frac{4\pi }{3} \end{cases}\implies A=\cfrac{\frac{4\pi }{3}(11)^2}{2}\implies A=\cfrac{\frac{484\pi }{3}}{2} \\\\\\ A=\cfrac{484\pi }{3}\cdot \cfrac{1}{2}\implies A=\cfrac{242\pi }{3}$