Question

arc cd is $\frac{2}{3}$ of the circumference of a circle. what is the radian measure of the central angle?$\bigcirc$ $\frac{2pi}{3}$ radians$\bigcirc$ $\frac{3pi}{4}$ radians$\bigcirc$ $\frac{4pi}{3}$ radians$\bigcirc$ $\frac{3pi}{2}$ radians

Explanation:

Step1: Recall full circle radians

A full circle has a central angle of $2\pi$ radians.

Step2: Calculate fraction of full angle

Multiply full circle radians by $\frac{2}{3}$.
$\text{Central angle} = \frac{2}{3} \times 2\pi$

Step3: Simplify the expression

Compute the product.
$\text{Central angle} = \frac{4\pi}{3}$

Answer:

$\boldsymbol{\frac{4\pi}{3}}$ radians (Option C)