Question

find the length of the arc, s, on a circle of radius r intercepted by a central angle θ. express the arc length in terms of π. then round your answer to two decimal p
radius, r = 10 inches; central angle, θ = 30°
s = inches
(simplify your answer. type an exact answer in terms of π. use integers or fractions for any numbers in the expression.)
s = inches
(round to two decimal places as needed.)

Explanation:

Step1: Convert angle to radians

First, convert the central - angle from degrees to radians. We know that to convert degrees to radians, we use the formula $\theta_{rad}=\theta_{deg}\times\frac{\pi}{180}$. Given $\theta = 30^{\circ}$, then $\theta_{rad}=30\times\frac{\pi}{180}=\frac{\pi}{6}$ radians.

Step2: Use the arc - length formula

The formula for the arc - length $s$ of a circle is $s = r\theta$, where $r$ is the radius of the circle and $\theta$ is the central angle in radians. Given $r = 10$ inches and $\theta=\frac{\pi}{6}$ radians, then $s=10\times\frac{\pi}{6}=\frac{5\pi}{3}$ inches.

Step3: Round the answer

To round $\frac{5\pi}{3}$ to two decimal places, we know that $\pi\approx3.14159$. So, $s=\frac{5\times3.14159}{3}\approx5.24$ inches.

Answer:

$s=\frac{5\pi}{3}$ inches
$s = 5.24$ inches