An arc has length 10π and corresponds to a central angle of 100°. What is the radius of the circle?

The arc length is the fraction $\frac{100}{360}=\frac{5}{18}$ of the circumference, so $10\pi=\frac{5}{18}(2\pi r)=\frac{5\pi r}{9}$. Multiply both sides by $\frac{9}{5\pi}$: $r=\frac{10\pi\cdot9}{5\pi}=18$, choice B. Check: the circumference is $36\pi$, and $\frac{5}{18}\cdot36\pi=10\pi$. Choice A ($10$) treats the arc length as if it equaled the radius times $\pi$ without using the angle. Choice C ($36$) is the diameter, twice the correct radius. Choice D ($100$) simply reuses the angle measure. Work from arc $=\frac{\theta}{360}\cdot2\pi r$.