Question

a circle has an arc length of 15 centimeters and a central angle of π radians. what is the radius of the circle? use the keypad to enter your answer in the box. express your answer to the nearest hundredth. the radius of the circle is centimeters

Explanation:

Step1: Recall arc - length formula

The formula for arc - length $s$ of a circle is $s = r\theta$, where $s$ is the arc - length, $r$ is the radius, and $\theta$ is the central angle in radians.

Step2: Rearrange formula for radius

We know that $s = 15$ cm and $\theta=\frac{\pi}{6}$ radians. Rearranging the formula $s = r\theta$ for $r$ gives $r=\frac{s}{\theta}$.

Step3: Substitute values

Substitute $s = 15$ and $\theta=\frac{\pi}{6}$ into the formula $r=\frac{s}{\theta}$. So $r=\frac{15}{\frac{\pi}{6}}$.

Step4: Simplify the expression

Using the rule of dividing by a fraction ($a\div\frac{b}{c}=a\times\frac{c}{b}$), we have $r = 15\times\frac{6}{\pi}=\frac{90}{\pi}\approx28.65$ cm.

Answer:

$28.65$