Question

Find the area of a sector of a circle whose central angle measures π/4 radians and whose radius is 4 cm. Express In terms of π and as a decimal.

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=4\\ \theta =(\pi )/(4) \end{cases}\implies A=\cfrac{ ~~ (\pi )/(4) ~~ (4)^2}{2}\implies A=2\pi \implies A\approx 6.28`