Step 1: Understanding the Question:
The question asks for the total angle (in degrees) that the hour hand of a standard clock sweeps across over a specific period.
The starting time is exactly 8:00 AM.
The ending time is exactly 2:00 PM on the same day.
Step 2: Key Formula or Approach:
The face of a clock is a full circle, measuring exactly $360^\circ$.
The hour hand takes 12 hours to complete one full $360^\circ$ rotation.
Therefore, the speed of the hour hand is $\frac{360}{12} = 30^\circ$ per hour.
We just need to calculate the elapsed time in hours and multiply it by $30^\circ$.
Step 3: Detailed Explanation:
First, we determine the total elapsed time between 8:00 AM and 2:00 PM.
From 8:00 AM to 12:00 Noon is a duration of 4 hours.
From 12:00 Noon to 2:00 PM is a duration of 2 hours.
Adding these together, the total elapsed time is $4 + 2 = 6$ hours.
We know that the hour hand rotates precisely $30^\circ$ for every passing hour.
To find the total rotation, we multiply the total hours by the angle per hour.
Total rotation $= 6 \text{ hours} \times 30^\circ/\text{hour} = 180^\circ$.
Since 6 hours represents exactly half of a 12-hour dial, the hand must have moved exactly half of a circle, which is a straight line or $180^\circ$.
Step 4: Final Answer:
The hour hand will rotate through 180 degrees.