Question

the radius of a circle measures 7 inches. a central angle of the circle measuring 4pi/15 radians cuts off a sector. what is the area of the sector? Enter your answer as simplified fraction in the box.

Answer 1

`\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta r^2}{2} ~~ \begin{cases} r=radius\\ \theta =\stackrel{radians}{angle}\\[-0.5em] \hrulefill\\ r=7\\ \theta =(4\pi )/(15) \end{cases}\implies A=\cfrac{ ~~ (4\pi )/(15)(7)^2}{2}\implies A=\cfrac{98\pi }{15}`