Question

calcule a area de um setor circular de raio 4cm e angulo central medindo 240º

Answer 1

$\mathbf{Convertendo\ de\ graus\ para\ radianos:}\\\\ \mathrm{240\°=270\°-30\°=\dfrac{3\pi}{2}-\dfrac{\pi}{6}=\dfrac{9\pi-\pi}{6}=\dfrac{8\pi}{6}=\dfrac{4\pi}{3}\ rd}\\\\ \mathbf{Calculando\ a\ \acute{a}rea\ do\ setor\ circular:}\\\\ \mathrm{A=\theta\dfrac{r^2}{2}=\dfrac{4\pi}{3}.\dfrac{4^2}{2}=\dfrac{2\pi}{3}.16=\dfrac{32\pi}{3}\ \to\ \boxed{\mathbf{A=\dfrac{32\pi}{3}\ cm^2}}}$