Find the radian measure of the central angle of the circle of radius 6 centimeters that intercepts an arc of length 32 centimeters.
A) $\theta = \frac { 16 } { 3 }$
B) $\theta = \frac { 2 } { 3 }$
C) $\theta = \frac { 3 } { 16 }$
D) $\theta = \frac { 32 } { 7 }$
E) $\theta = \frac { 6 } { 5 }$

Question

Quizplus · Accepted Answer

The radian measure of a central angle ($\theta$) is given by the formula $\theta = \frac{l}{r}$, where $l$ is the length of the intercepted arc and $r$ is the radius of the circle. Substituting $l = 32$ cm and $r = 6$ cm gives $\theta = \frac{32}{6} = \frac{16}{3}$.

Find the Radian Measure of the Central Angle of the Circle