Respuesta :

semsee45

Answer:

B.  [tex]4\pi[/tex]

Step-by-step explanation:

[tex]\mathsf{arc \ length=\dfrac{2\pi r\theta}{360}}[/tex]

(where [tex]\theta[/tex] is the angle of the sector measured in degrees and r is the radius)

[tex]\implies \mathsf{arc \ length=\dfrac{2\pi \cdot 18 \cdot 40}{360}=\dfrac{1440\pi}{360}=4\pi}[/tex]

Convert theta to radians

  • 40°
  • 40π/180
  • 2π/9

Now

[tex]\\ \rm\rightarrowtail L=r\theta[/tex]

[tex]\\ \rm\rightarrowtail L=18(2\pi/9)[/tex]

[tex]\\ \rm\rightarrowtail L=4\pi[/tex]

Option B is correct

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