Through how many radians will the hour hand on a clock rotate in ​(a) 19 ​hr? In Bold left parenthesis b right parenthesis 6 hr question mark


The hour hand on a clock completes one full rotation (360 degrees) in 12 hours, which is equivalent to \(2\pi\) radians. To calculate the radians for any number of hours, we use the ratio:

\[
\text{radians per hour} = \frac{2\pi \text{ radians}}{12 \text{ hours}} = \frac{\pi}{6} \text{ radians per hour}.
\]

### (a) For 19 hours:

\[
\text{radians in 19 hours} = 19 \times \frac{\pi}{6} = \frac{19\pi}{6} \text{ radians}.
\]

### (b) For 6 hours:

\[
\text{radians in 6 hours} = 6 \times \frac{\pi}{6} = \pi \text{ radians}.
\]

### Final answers:
- (a) \( \frac{19\pi}{6} \) radians
- (b) \( \pi \) radians

Would you like more details or have any questions?  
Here are 5 related questions to explore further:
1. How many degrees does the hour hand rotate in 24 hours?
2. What is the radian measure for 3 hours of rotation?
3. How many hours does it take for the hour hand to rotate \(2\pi\) radians?
4. How many radians will the minute hand rotate in 45 minutes?
5. What fraction of a full rotation does the hour hand complete in 9 hours?

**Tip:** To convert from degrees to radians, multiply by \( \frac{\pi}{180} \).

Through how many radians will the hour hand on a clock rotate in (a) 19 hr? (b) 6 hr?

Discover how to calculate the radians the hour hand on a clock rotates in 19 and 6 hours. This problem explains the relationship between time and angles, using the formula radians = π/6 per hour. Suitable for Grades 7-9 students learning basic trigonometry and radian measures.

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