The minute hand of a clock moves from 12 to

8

​o'clock, or

two thirds

of a complete revolution.  Through how many degrees does it​ move?  Through how many radians does it​ move?

To solve this problem, let's break it down into two parts: calculating the movement in degrees and in radians.

### 1. Movement in Degrees
The minute hand of a clock makes a complete revolution of \(360^\circ\) when it moves from 12 back to 12. The problem states that the minute hand moves from 12 to 8 o'clock, which is \(\frac{2}{3}\) of a complete revolution.

\[
\text{Degrees moved} = \frac{2}{3} \times 360^\circ = 240^\circ
\]

So, the minute hand moves through **240 degrees**.

### 2. Movement in Radians
Radians are another way to measure angles. One complete revolution is equal to \(2\pi\) radians.

\[
\text{Radians moved} = \frac{2}{3} \times 2\pi \text{ radians} = \frac{4\pi}{3} \text{ radians}
\]

So, the minute hand moves through **\(\frac{4\pi}{3}\) radians**.

### Final Answers:
- The minute hand moves through **240 degrees**.
- The minute hand moves through **\(\frac{4\pi}{3}\) radians**.

Would you like more details or have any questions?

#### Related Questions:
1. What is the angular speed of the minute hand in radians per second?
2. How many degrees does the minute hand move in 5 minutes?
3. How many radians does the hour hand move in 4 hours?
4. If the clock is a 24-hour clock, how many degrees does the minute hand move from 12 to 18 o'clock?
5. What is the relationship between degrees and radians in a full revolution?

#### Tip:
Remember, \(180^\circ\) is equal to \(\pi\) radians, which is a key conversion factor between degrees and radians.

Understand how many degrees and radians the minute hand of a clock moves from 12 to 8 o'clock. This problem explores the conversion between degrees and radians, suitable for Grades 6-8.

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