Find the arc length with the given information.

Question

central angle equals Start Fraction pi over 4 End Fraction, radius = 3
(1 point)
Responses

Start Fraction 3 pi over 2 End Fraction
Image with alt text: Start Fraction 3 pi over 2 End Fraction

Start Fraction 3 pi over 4 End Fraction
Image with alt text: Start Fraction 3 pi over 4 End Fraction

Start Fraction pi over 6 End Fraction
Image with alt text: Start Fraction pi over 6 End Fraction

Start Fraction pi over 12 End Fraction

Answer 1

To find the arc length \( L \) of a circle corresponding to a central angle, you can use the formula:

\[ L = r \theta \]

where:

• \( r \) is the radius of the circle,
• \( \theta \) is the central angle in radians.

Given:

• \( r = 3 \)
• \( \theta = \frac{\pi}{4} \)

Now, substituting the values into the formula:

\[ L = 3 \cdot \frac{\pi}{4} = \frac{3\pi}{4} \]

So the arc length is:

\[ \frac{3\pi}{4} \]

The correct response is:

\[ \text{Start Fraction } 3 \pi \text{ over } 4 \text{ End Fraction} \]