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 =(\pi )/(4) \end{cases}\implies A=\cfrac{(\pi )/(4)\cdot 3^2}{2}\implies A=\cfrac{(9\pi )/(4)}{2} \\\\\\ A=\cfrac{9\pi }{4}\cdot \cfrac{1}{2}\implies A=\cfrac{9\pi }{8}`