Question

which expression represents the length in centimeters of $widehat{ac}$?
o a) $\frac{7}{10}pi$
o b) $\frac{7}{5}pi$
o c) $\frac{63}{4}pi$
o d) $\frac{63}{2}pi$

Explanation:

Step1: Recall arc - length formula

The formula for the length of an arc $s$ of a circle with radius $r$ and central - angle $\theta$ (in degrees) is $s=\frac{\theta}{360}\times2\pi r$.

Step2: Identify values of $\theta$ and $r$

Here, $\theta = 63^{\circ}$ and $r = 4$ cm.

Step3: Substitute values into formula

$s=\frac{63}{360}\times2\pi\times4$.
First, simplify $\frac{63}{360}=\frac{7}{40}$, then $s=\frac{7}{40}\times2\pi\times4$.
$\frac{7}{40}\times2\pi\times4=\frac{7\times2\times4\pi}{40}=\frac{56\pi}{40}=\frac{7}{5}\pi$.

Answer:

B. $\frac{7}{5}\pi$