SAT Question 149021da: Circles answer and explanation with Desmos solution

It’s given that the measure of arc $AB$ is $45^{\circ }$ and the length of arc $AB$ is $4\pi$ units. In a circle, the circumference corresponds to an arc measure of $360^{\circ }$. Therefore, the ratio of the measure of arc $AB$ to $360^{\circ }$ is equal to the ratio of the length of arc $AB$ to the circumference. Since the circumference of a circle is $2\pi r$, it follows that $\frac{45}{360}=\frac{4\pi }{2\pi r}$. This equation can be rewritten as $\frac{1}{8}=\frac{2}{r}$. Multiplying both sides of this equation by $8r$ yields $1(r)=2(8)$, or $r=16$. Therefore, the length, in units, of the radius of the circle is $16$.