find the length of arc abc. use 3.14 for the value of π. round to the nearest hundredth of a cm.

Explanation:

Step1: Recall arc - length formula

The formula for the length of an arc of a circle is $s = r\theta$, where $r$ is the radius of the circle and $\theta$ is the central - angle in radians. First, convert the angle from degrees to radians. We know that $1^{\circ}=\frac{\pi}{180}$ radians. So, if $\theta = 270^{\circ}$, then $\theta=270\times\frac{\pi}{180}=\frac{3\pi}{2}$ radians, and $r = 52$ cm.

Step2: Calculate the arc - length

Substitute $r = 52$ cm and $\theta=\frac{3\pi}{2}$ into the arc - length formula $s=r\theta$. So, $s = 52\times\frac{3\pi}{2}$. [ \begin{align*} s&=52\times\frac{3\pi}{2}\ &= 78\pi \end{align*} ] Substitute $\pi = 3.14$ into the equation: $s=78\times3.14 = 244.92$ cm.

Answer:

$244.92$ cm