[tex] \bf \textit{arc's length}\\\\
s=r\theta ~~
\begin{cases}
r=radius\\
\theta =angle~in\\
\qquad radians\\
------\\
s=32\\
\theta =\pi
\end{cases}\implies 32=r\pi \implies \cfrac{32}{\pi }=r [/tex]
Answer: b. 10.2 in.
Step-by-step explanation:
We know that the formula to calculate the length of arc is given by :-
[tex]l=\theta\times r[/tex]
Given : The central angle : [tex]\theta=\pi[/tex]
The length of arc : [tex]l=32\text{ inches}[/tex]
[tex]\Rightarrow32=\pi\times r\\\\\Rightarrow\ r=\dfrac{32}{\pi}=10.18591635\approx10.2\text{inches}[/tex]
Hence, the radius of the circle =10.2 inches.
