Question

If a circular pool has a circular fence around it that has a 20-foot diameter, then what is the measure of the central angle that cuts the arc that measures 4 feet?(1 point)
Responses

226.2 degrees
226.2 degrees

22.9 degrees
22.9 degrees

45.8 degrees
45.8 degrees

72 degrees

Answer 1

To find the measure of the central angle that corresponds to an arc length of 4 feet on a circular pool with a diameter of 20 feet, we can use the formula for arc length:

\[
L = r \theta
\]

where \( L \) is the arc length, \( r \) is the radius, and \( \theta \) is the central angle in radians.

1. First, calculate the radius of the circular pool:
\[
r = \frac{\text{diameter}}{2} = \frac{20 \text{ feet}}{2} = 10 \text{ feet}
\]

2. Now, we set up the equation for arc length:
\[
4 \text{ feet} = 10 \text{ feet} \cdot \theta
\]

3. Solve for \(\theta\):
\[
\theta = \frac{4 \text{ feet}}{10 \text{ feet}} = 0.4 \text{ radians}
\]

4. To convert radians to degrees, we use the conversion factor \( \frac{180}{\pi} \):
\[
\theta = 0.4 \text{ radians} \times \frac{180}{\pi} \approx 22.9 \text{ degrees}
\]

Thus, the measure of the central angle that cuts the arc that measures 4 feet is **22.9 degrees**.