The formula for the length of an arc of a sector is :
[tex]L=\frac{\theta}{360}\times2\pi r[/tex]where:
[tex]\begin{gathered} \theta=\sec tor\text{ angle} \\ r=\text{radius of the circle} \end{gathered}[/tex]Since we are given:
[tex]\begin{gathered} \theta=48^o \\ r=15\operatorname{cm} \end{gathered}[/tex]we have that:
[tex]\begin{gathered} L=\frac{\theta}{360}\times2\pi r \\ \Rightarrow L=\frac{48}{360}\times2\pi(15) \end{gathered}[/tex][tex]L=\frac{2}{15}\times30\pi[/tex][tex]\Rightarrow L=\frac{60\pi}{15}[/tex][tex]\Rightarrow L=4\pi[/tex][tex]\begin{gathered} \Rightarrow L=4\times3.14=12.56 \\ \Rightarrow L=12.6\text{ cm} \end{gathered}[/tex]Thus, correct answer: Option B
