Question

Use the fact that the length of an arc intercepted by an angle is proportional to the radius to find the area of the sector given r = 3 cm and Θ = π/4

Answer 1

$\bf \textit{area of a sector of a circle}\\\\ A=\cfrac{\theta r^2}{2}~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad radians\\ ------\\ r=3\\ \theta =\frac{\pi }{4} \end{cases}\implies A=\cfrac{\frac{\pi }{4}\cdot 3^2}{2}\implies A=\cfrac{\frac{9\pi }{4}}{2} \\\\\\ A=\cfrac{9\pi }{4}\cdot \cfrac{1}{2}\implies A=\cfrac{9\pi }{8}$