Question

1. find the length of the radius in the diagram below.

$\frac{7pi}{2}$yd
$\frac{pi}{4}$

Explanation:

Step1: Recall arc - length formula

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

Step2: Identify given values

We are given that $s=\frac{7\pi}{2}$ yd and $\theta=\frac{\pi}{4}$.

Step3: Solve for $r$

Substitute the given values into the formula $s = r\theta$: $\frac{7\pi}{2}=r\times\frac{\pi}{4}$.
To solve for $r$, we can multiply both sides of the equation by $\frac{4}{\pi}$.
$r=\frac{7\pi}{2}\times\frac{4}{\pi}$.
The $\pi$ terms cancel out, and we have $r = 14$ yd.

Answer:

$14$ yd