An accurate clock indicates 8 O' clock in the morning. Through how many degrees the hour hand turns when the clock indicates 3 O' clock in the afternoon?

1. Break Down the Problem

We need to find out the total degrees the hour hand of a clock moves from 8:00 AM to 3:00 PM.

2. Relevant Concepts

The clock is a circle, and the hour hand moves 360 degrees in 12 hours. Therefore, the degrees moved per hour can be calculated using the formula: $\text{Degrees per hour} = \frac{360 \text{ degrees}}{12 \text{ hours}} = 30 \text{ degrees/hour}$

3. Analysis and Detail

1. Calculate the time from 8:00 AM to 3:00 PM: $\text{Time elapsed} = 3:00 PM - 8:00 AM = 7 \text{ hours}$

2. Now, calculate the degrees turned by the hour hand in these 7 hours: $\text{Degrees turned} = 7 \text{ hours} \times 30 \text{ degrees/hour} = 210 \text{ degrees}$

4. Verify and Summarize

The calculations are verified, showing that for every hour, the hour hand moves 30 degrees. In 7 hours, it turns 210 degrees.

Final Answer

The hour hand turns a total of $210$ degrees when the clock indicates 3 O' clock in the afternoon.