Question

Il 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)
• 226.2 degrees
• 72 degrees
45.8 degrees
22.9 degrees

Answer 1

To find the central angle that cuts the arc measuring 4 feet in a circular pool with a diameter of 20 feet, we first need to calculate the circumference of the pool.

1. **Calculate the radius**:
The radius \( r \) is half of the diameter.
\[
r = \frac{20}{2} = 10 \text{ feet}
\]

2. **Calculate the circumference**:
The formula for the circumference \( C \) of a circle is:
\[
C = 2\pi r
\]
Substituting the radius:
\[
C = 2\pi (10) = 20\pi \text{ feet}
\]

3. **Calculate the central angle**:
The central angle \( \theta \) in radians corresponding to an arc length \( s \) can be found using the formula:
\[
\theta = \frac{s}{r}
\]
Here, \( s = 4 \) feet and \( r = 10 \) feet.
\[
\theta = \frac{4}{10} = 0.4 \text{ radians}
\]

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

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