Question

which equation gives the length of an arc, s, intersected by a central angle of 3 radians in a circle with a radius of 4 in.?
○ $s=\frac{3}{4}$
○ $s=\frac{4}{3}$
○ $s=4+3$
○ $s=4\cdot 3$

Explanation:

Step1: Recall arc length formula

The formula for the length of an arc \( s \) when the central angle \( \theta \) is in radians is \( s = r\theta \), where \( r \) is the radius of the circle.

Step2: Identify values

Here, the radius \( r = 4 \) in and the central angle \( \theta = 3 \) radians.

Step3: Substitute values

Substitute \( r = 4 \) and \( \theta = 3 \) into the formula \( s = r\theta \). So, \( s = 4\times3 \) (or \( s = 4\cdot3 \) as in the option).

Answer:

\( s = 4\cdot3 \) (the last option, assuming the dot is a multiplication symbol)