A central angle of a circle that measure pi/3 radians intercepts an arc that is 12 cm. What is the radius of the circle?

Question

$\frac{π}{3}$ $pi/3$

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Answer 1 · 2018-05-17T03:06:25

$r = \frac{36}{π} cm$ $r = 36/pi" cm"$

Given $s = 12 cm$ $s=12" cm"$ where $s$ $s$ is the arclength and $θ = \frac{π}{3}$ $theta = pi/3$ where $θ$ $theta$ is the central angle.

The following equation describes their relationship to the radius:

$s = r θ$ $s = r theta$

Solve for $r$ $r$ :

$r = \frac{s}{θ}$ $r = s/theta$

Substitute the values:

$r = \frac{12 cm}{\frac{π}{3}}$ $r = (12" cm")/(pi/3)$

$r = \frac{36}{π} cm$ $r = 36/pi" cm"$