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 \times 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 Given Values

Here, \( r = 4 \) inches and \( \theta = 3 \) radians.

Step3: Substitute Values into 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 last option is \( s = 4 \cdot 3 \) with proper multiplication notation)