If the radius of a circle is 10 feet and the central angle is 3π4, then what is the arc length in radians?(1 point) Responses 15π 15 pi 60π 60 pi 30π 30 pi 15π2

Answer 1

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

\[ L = r \theta \]

where \( r \) is the radius and \( \theta \) is the central angle in radians.

Given:

• Radius \( r = 10 \) feet
• Central angle \( \theta = \frac{3\pi}{4} \)

Now plug in the values:

\[ L = 10 \times \frac{3\pi}{4} = \frac{30\pi}{4} = \frac{15\pi}{2} \]

So, the arc length is:

\[ \frac{15\pi}{2} \]

Therefore, the correct answer from your options is 15π2.