Question

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

Use 3.14 for pi and round to the nearest hundredth

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 =(4\pi )/(3) \end{cases}\implies A=\cfrac{(4\pi )/(3)(11)^2}{2}\implies A=\cfrac{(484\pi )/(3)}{2} \\\\\\ A=\cfrac{484\pi }{3}\cdot \cfrac{1}{2}\implies A=\cfrac{242\pi }{3}`