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The question in the image asks:

**What is the central angle, in degrees, that corresponds to an arc length of 16 inches, given that the diameter of the circle is 48 inches? Round off your answer to the nearest whole number.**

### Solution:

1. **Determine the radius of the circle**:
   The diameter of the circle is 48 inches, so the radius \( r \) is:
   \[
   r = \frac{\text{diameter}}{2} = \frac{48}{2} = 24 \text{ inches}
   \]

2. **Use the formula for arc length**:
   The arc length \( L \) of a circle is related to the central angle \( \theta \) (in radians) by the formula:
   \[
   L = r \theta
   \]
   We know \( L = 16 \) inches and \( r = 24 \) inches, so:
   \[
   16 = 24 \theta
   \]

3. **Solve for \( \theta \)** (in radians):
   \[
   \theta = \frac{16}{24} = \frac{2}{3} \text{ radians}
   \]

4. **Convert radians to degrees**:
   To convert radians to degrees, use the conversion factor \( 180^\circ / \pi \):
   \[
   \theta = \frac{2}{3} \times \frac{180^\circ}{\pi} \approx 38.197 \text{ degrees}
   \]

5. **Round to the nearest whole number**:
   The central angle is approximately:
   \[
   \theta \approx 38^\circ
   \]

### Final Answer: 
The central angle is approximately **38 degrees**.

Would you like further clarification or details on this solution?

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Here are 5 related questions to explore:

1. How does the formula for arc length change if the angle is given in degrees?
2. What would the central angle be if the arc length was 24 inches, keeping the same diameter?
3. How do you calculate the area of a sector of a circle with a given central angle?
4. How is the circumference of a circle related to its diameter and radius?
5. What is the radian measure of a full circle, and why is it used in arc length calculations?

**Tip**: Always remember to convert between radians and degrees using the conversion factor \( \pi \text{ radians} = 180^\circ \).

What is the central angle, in degrees, that corresponds to an arc length of 16 inches, given that the diameter of the circle is 48 inches? Round off your answer to the nearest whole number.

Learn how to calculate the central angle in degrees for a circle with an arc length of 16 inches and a diameter of 48 inches. This problem involves key geometric concepts like arc length, radians, and the conversion to degrees. Ideal for students in Grades 9-12.

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