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Answer:
[tex]1.5\pi[/tex] cm
Step-by-step explanation:
A central angle measuring [tex]45^\circ[/tex] is [tex]\frac{45^\circ}{360^\circ}=\frac{45}{360}[/tex], or [tex]\frac{1}{8}[/tex] of the entire circle. The circumference of the circle is given by the formula [tex]2\pi r[/tex], which is [tex]12\pi[/tex].
Then, the length of an arc measuring [tex]\frac{1}{8}[/tex] of the entire circle is [tex]12\pi\cdot\frac{1}{8}=1.5\pi[/tex] cm.