a circle has a central angle measuring $\frac{7pi}{10}$ radians that intersects an arc of length 33 cm. what…

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. We are given that $s = 33$ cm and $\theta=\frac{7\pi}{10}$ radians.

Step2: Solve for the radius $r$

From $s = r\theta$, we can express $r$ as $r=\frac{s}{\theta}$. Substitute $s = 33$ and $\theta=\frac{7\pi}{10}$ into the formula: $r=\frac{33}{\frac{7\pi}{10}}=\frac{33\times10}{7\pi}$. Since $\pi = 3.14$, we have $r=\frac{330}{7\times3.14}=\frac{330}{21.98}\approx15$ cm.

Answer:

15 cm