Middle School

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Find the radius of a circle if a central angle of [tex]\pi[/tex] intercepts an arc of 32 inches. Round to the nearest tenth.

a. 3.1 in.
b. 10.2 in.
c. 100.5 in.

Answer :

[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]

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Rewritten by : Barada

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.