Question

If the radius of a circle is 10 feet and the central angle is 3π/4, then what is the arc length in radians?

a. 60π
b. 30π
c. 15π/2
d. 15π

Answer 1

The formula for the arc length \( L \) of a circle is given by:

\[
L = r \theta
\]

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

Given:
- Radius \( r = 10 \) feet
- Central angle \( \theta = \frac{3\pi}{4} \) radians

Substituting the values into the formula:

\[
L = 10 \cdot \frac{3\pi}{4}
\]

Calculating this gives:

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

So, the arc length is:

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

Thus, the answer is:

**c. \( \frac{15\pi}{2} \)**.