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 = 3/4
○ s = 4/3
○ s = 4 + 3
○ s = 4 3

Explanation:

Step1: Recall arc length formula

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

Step2: Identify values of \( r \) and \( \theta \)

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

Step3: Substitute values into the formula

Substituting \( r = 4 \) and \( \theta = 3 \) into \( s = r\theta \), we get \( s = 4\times3 \) (or \( s = 4\cdot3 \)).

Answer:

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