Question

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. Given $\theta=90^{\circ}$, and since $180^{\circ}=\pi$ radians, then $90^{\circ}=\frac{\pi}{2}$ radians, and $r = 58$ cm.

Step2: Substitute values into the formula

Substitute $r = 58$ cm and $\theta=\frac{\pi}{2}$ into the arc - length formula $s=r\theta$. So $s=58\times\frac{\pi}{2}$.

Step3: Calculate the arc length

Since $\pi = 3.14$, we have $s = 58\times\frac{3.14}{2}=58\times1.57$. Then $s = 91.06$ cm.

Answer:

$91.06$ cm