Question

What is the area
of a sector
when 0=pi/2 radians and
8/
3?

Answer 1

`\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta r^2}{2}~~ \begin{cases} r=radius\\ \theta =\stackrel{radias}{angle}\\[-0.5em] \hrulefill\\ r=(8)/(3)\\ \theta =(\pi )/(2) \end{cases}\implies A=\cfrac{~~ \left( (\pi )/(2) \right)\left( (8)/(3) \right)^2~~}{2}\implies A=\cfrac{~~ \left( (\pi )/(2) \right)\left( (64)/(9) \right)~~}{2} \\\\\\ A=\cfrac{~~(32\pi )/(9) ~~}{(2)/(1)}\implies A=\cfrac{32\pi }{9}\cdot \cfrac{1}{2}\implies A=\cfrac{16\pi }{9}`