Question

a circle has a central angle of 6 radians that intersects an arc of length 14 in. which equation finds the length of the radius, r, of the circle?
( r=\frac{6}{14} )
( r=\frac{14}{6} )
( r = 6+14 )
( r = 614 )

Explanation:

Step1: Recall arc length formula

The formula for the length of an arc \( s \) in a circle with central angle \( \theta \) (in radians) and radius \( r \) is \( s = r\theta \).

Step2: Solve for radius \( r \)

We are given \( s = 14 \) and \( \theta = 6 \). From \( s = r\theta \), we can solve for \( r \) by dividing both sides of the equation by \( \theta \). So, \( r=\frac{s}{\theta} \). Substituting the given values \( s = 14 \) and \( \theta = 6 \), we get \( r=\frac{14}{6} \).

Answer:

\( r=\frac{14}{6} \) (corresponding to the option \( r=\frac{14}{6} \))