Question

What is the radius of a circle with a central angle of 4π/7 radians that intercepts an arc of length 12π inches?

Answer 1

Answer:

21 inches

Step-by-step explanation:

If $\alpha$ is the central angle, then the length of the arc on which this angle subtends is

$l=r\cdot \alpha.$

Hence,

$12\pi =\dfrac{4\pi}{7}\cdot r,\\ \\r=\dfrac{12\pi}{\frac{4\pi}{7}}=\dfrac{12\pi}{1}\cdot \dfrac{7}{4\pi}=21\ in.$