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# Find the radius of the circle in which a central angle of $45^{\large\circ}$ intercepts an arc 132cm

$\begin{array}{1 1}(A)\;150cm&(B)\;160cm\\(C)\;168cm&(D)\;178cm\end{array}$

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Toolbox:
• Radian measure =$\large\frac{\pi}{180}\times$ Degree measure
• $\theta=\large\frac{l}{r}$
Here
$l=132cm$
$\theta=45^{\large\circ}$
Radian measure =$45\times \large\frac{\pi}{180}$
$\Rightarrow \large\frac{\pi}{4}$ radians
Now,by $r=\large\frac{l}{\theta}$
We have
$r=132\times \large\frac{4}{\pi}$cm
$\Rightarrow 132\times 4\times \large\frac{7}{22}$cm
$\Rightarrow 168$cm
Hence (C) is the correct answer.
answered May 20, 2014