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:

$$\text{Start Fraction }3\pi \text{ over }4\text{ End Fraction}$$