The radius of a circle is 50 cm. Find the angle subtends by an arc of 22 cm length at the centerof the circle.

Options

A. `25 degree 12 min`
B. 25 degree 30 min
C. 30 degree 12 min
D. 35 degree 12 min

Explanation

To find the angle subtended by an arc of length 22 cm at the center of a circle with a radius of 50 cm, we can use the formula that relates the arc length (s), the radius (r), and the angle (θ) in radians:

\[ \theta = \frac{s}{r} \]

### Step-by-Step Solution:

1. **Identify the given values**:
- Arc length (s) = 22 cm
- Radius (r) = 50 cm

2. **Use the formula to find the angle in radians**:
\[ \theta = \frac{s}{r} = \frac{22}{50} \]
\[ \theta = 0.44 \text{ radians} \]

3. **Convert the angle from radians to degrees**:
To convert radians to degrees, we use the conversion factor \( \frac{180}{\pi} \):
\[ \theta_{degrees} = \theta_{radians} \times \frac{180}{\pi} \]
\[ \theta_{degrees} = 0.44 \times \frac{180}{\pi} \approx 0.44 \times 57.2958 \approx 25.4 \text{ degrees} \]

4. **Convert the decimal part of degrees to minutes**:
The decimal 0.4 degrees can be converted to minutes:
\[ 0.4 \text{ degrees} \times 60 \text{ minutes/degree} = 24 \text{ minutes} \]

5. **Combine the degrees and minutes**:
Thus, the angle subtended by the arc at the center of the circle is:
\[ 25 \text{ degrees and } 24 \text{ minutes} \]

### Final Answer:
The angle subtended by the arc of length 22 cm at the center of the circle is approximately **25 degrees and 24 minutes**.