If a circle has a radius of 6 cm and a central angle of 5π4 , then what is the length of the arc created by the angle?(1 point)

Answer 1

To find the length of the arc created by a central angle in a circle, we can use the formula:

$$\text{Arc Length}=r\theta$$

where:

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

Given:

• Radius $r=6$ cm,
• Central angle $\theta =\frac{5\pi }{4}$ radians.

Now, substituting these values into the formula:

$$\text{Arc Length}=6\cdot \frac{5\pi }{4}$$

Calculating this, we have:

$$\text{Arc Length}=\frac{6\cdot 5\pi }{4}=\frac{30\pi }{4}=\frac{15\pi }{2}$$

Thus, the length of the arc is:

$$\frac{15\pi }{2}\text{ cm}$$

So, the final answer is:

$\frac{15\pi }{2}$ cm.