Question

Considere o segmento circular com α = 60◦. Calcule sua área sabendo que o raiomede 2cm. Qual a área do setor circular?

Answer 1

Resposta:

$a)A=(\frac{2\pi }{3}-\sqrt{3})~cm^2 \\\\b)A=\frac{2\pi }{3}~cm^2$

Explicação passo a passo:

$Area~~do~~triangulo\\\\A=\frac{r^2}{2}*sen60\° \\\\A=\frac{2^2}{2}*\frac{\sqrt{3} }{2} \\\\A=\sqrt{3}~~ cm^2\\\\Area~~ do~~setor~~AOB\\\\A=\frac{\pi r^2.60}{360} \\\\A=\frac{\pi *2^2}{6} \\\\A=\frac{4\pi }{6} \\\\A=\frac{2\pi }{3}~cm^2\\\\Area~do~segmentocircular\\\\A=A_s_e_t_o_r -A__t_r_i_a_n_g.$

$A=(\frac{2\pi }{3}-\sqrt{3})~cm^2$