Question

a circle has a radius of 9 units. if a central - angle, ∠ghi, measures $\frac{3pi}{2}$ radians, what is the length of the intercepted arc $widehat{gi}$? use the keypad to enter your answer in the box. express your answer in the simplest fraction. the length of $widehat{gi}$ is units

Explanation:

Step1: Recall arc - length formula

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

Step2: Identify given values

We are given that $r = 9$ units and $\theta=\frac{3\pi}{2}$ radians.

Step3: Substitute values into formula

Substitute $r = 9$ and $\theta=\frac{3\pi}{2}$ into the formula $s = r\theta$. So, $s=9\times\frac{3\pi}{2}=\frac{27\pi}{2}$ units.

Answer:

$\frac{27\pi}{2}$