Question

3 the diameter of a circle is 8 centimeters. a central angle of the circle intercepts an arc of 12 centimeters. what is the radian measure of the angle? a \\(\frac{3}{2}\\) c 4 b 3 d \\(8\pi\\) \\(\bigcirc\\) c \\(\bigcirc\\) d \\(\bigcirc\\) b \\(\bigcirc\\) a

Explanation:

Step1: Find the radius

The diameter \( d = 8 \) cm, so the radius \( r=\frac{d}{2}=\frac{8}{2} = 4 \) cm.

Step2: Use the arc - length formula

The formula for the length of an arc \( s \) intercepted by a central angle \( \theta \) (in radians) in a circle of radius \( r \) is \( s = r\theta \). We know that \( s = 12 \) cm and \( r = 4 \) cm.
We can solve for \( \theta \) by rearranging the formula: \( \theta=\frac{s}{r} \).
Substitute \( s = 12 \) and \( r = 4 \) into the formula: \( \theta=\frac{12}{4}=3 \).

Answer:

B. 3