The central angle of a sector is 80° and whose length is 96π. What is the radius of the circle?

To find the radius of the circle, we can use the formula that relates the arc length of a sector, its central angle, and the radius of the circle.

The formula for the arc length ($s$) of a sector is given by:
$s=\frac{\theta }{360°}\times 2\pi r$
where:
- $s$ is the arc length of the sector,
- $\theta$ is the central angle in degrees, and
- $r$ is the radius of the circle.

From the given problem, we have:
- Central angle, $\theta =80°$
- Arc length, $s=96\pi$

Substituting these values into the formula, we get:
$96\pi =\frac{80°}{360°}\times 2\pi r$

Now, we can simplify the equation. First, divide both sides by $\pi$:
$96=\frac{80}{360}\times 2r$

Simplify the fraction $\frac{80}{360}$ by dividing the numerator and denominator by 40:
$\frac{80}{360}=\frac{2}{9}$

Substitute this back into the equation:
$96=\frac{2}{9}\times 2r$
$96=\frac{4}{9}r$

To solve for $r$, multiply both sides of the equation by $\frac{9}{4}$:
$r=96\times \frac{9}{4}$

Calculate the value:
$r=24\times 9$
$r=216$

Therefore, the radius of the circle is 216 units.