Question

find the arc - length of the sector of a circle with the given radius (r) and central angle (\theta). give the answer in the given unit of measure, rounded to the nearest hundredth.(r = 25 m;\theta=\frac{12pi}{7})

Explanation:

Step1: Recall 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.

Step2: Substitute given values

We are given $r = 25$ m and $\theta=\frac{12\pi}{7}$. Substitute these values into the formula: $s=25\times\frac{12\pi}{7}$.

Step3: Calculate the value

$s=\frac{300\pi}{7}\approx\frac{300\times 3.14159}{7}\approx134.59$ m.

Answer:

$134.59$ m