Find the radian measure of the central angle of a circle of radius $r$ that intercepts an arc of length $s$.
radius: $r = 12$ kilometers arc length: $s = 64$ kilometers
A) $\frac { 3 } { 16 }$

B) $\frac { 3 \pi } { 16 }$

C) $\frac { 16 \pi } { 3 }$

D) $\frac { 8 } { 3 }$

E) $\frac { 16 } { 3 }$

Question

Find the radian measure of the central angle of a circle of radius $r$ that intercepts an arc of length $s$.
radius: $r = 12$ kilometers arc length: $s = 64$ kilometers
A) $\frac { 3 } { 16 }$

B) $\frac { 3 \pi } { 16 }$

C) $\frac { 16 \pi } { 3 }$

D) $\frac { 8 } { 3 }$

E) $\frac { 16 } { 3 }$

Quizplus · Accepted Answer

The radian measure of a central angle ($\theta$) is given by the formula $\theta = \frac{s}{r}$, where $s$ is the arc length and $r$ is the radius of the circle. Substituting $s = 64$ km and $r = 12$ km, we get $\theta = \frac{64}{12} = \frac{16}{3}$.

Find the Radian Measure of the Central Angle of a Circle