Question

What is the radius of a circle that has a central angle of 12 radians and an arc length of 72 feet?

Answer 1

!2 radians correspond to $\frac{12}{2\pi}$ revolutions.
Circumference is the arc length of one revolution, given by:
$\frac{72}{\frac{12}{2\pi}}=12\pi$
$circumference=2\pi r$
$2\pi r=12\pi$
$r=\frac{12\pi}{2\pi}=6$
The answer is: the radius of the circle is 6 feet.