Respuesta:
B) 2
Explicación paso a paso:
S1 es el área del sector circular con amplitud angular desconocida ([tex]\alpha[/tex])
y radio desconocido ( r)
S1 = [tex]\frac{\pi r^{2}\alpha }{360}[/tex]
S2 es el segmento circular con R = 2r
S2 = [tex]\frac{\pi[ (2r)^{2}-r^{2}] \alpha }{360}=\frac{\pi [4r^{2}-r^{2}] }{360 } =\frac{\pi 3r^{2} }{360}[/tex]
S3 es el segmento circular con R = 3r y r menor = 2r
S3 = [tex]\frac{\pi[ (3r)^{2}-(2r)^{2}] \alpha }{360}=\frac{\pi [9r^{2}-4r^{2}] }{360 } =\frac{\pi 5r^{2} }{360}[/tex]
Luego [tex]M=\frac{S1+S3}{S2} =\frac{\frac{\pi r^{2}\alpha }{360}+\frac{\pi5r^{2}\alpha }{360} }{\frac{\pi 3r^{2} \alpha }{360} }=\frac{\frac{\pi 6r^{2}\alpha }{360} }{\frac{\pi 3r^{2}\alpha }{360} }= 2[/tex]
