Question

the second hand of a clock is 5 cm long. in one hour, the tip of the second hand travels a distance of...

Answer 1

To find the distance traveled by the tip of the second hand in one hour, we can first determine the distance it travels in one circle and then calculate how many circles it completes in an hour.

1. **Calculate the circumference of the circle traced by the second hand:**
The circumference \( C \) of a circle is given by the formula:
\[
C = 2 \pi r
\]
where \( r \) is the radius.

For the second hand, the length (radius) is 5 cm. Thus:
\[
C = 2 \pi \times 5 \, \text{cm} = 10 \pi \, \text{cm}
\]

2. **Determine how many complete rotations the second hand makes in one hour:**
The second hand completes one full rotation every 60 seconds. In one hour (which is 3600 seconds), the second hand completes:
\[
\text{Number of rotations} = \frac{3600 \, \text{seconds}}{60 \, \text{seconds/rotation}} = 60 \, \text{rotations}
\]

3. **Calculate the total distance traveled by the tip of the second hand in one hour:**
To find the total distance, multiply the distance of one rotation (the circumference) by the number of rotations:
\[
\text{Total distance} = 60 \times C = 60 \times 10 \pi \, \text{cm} = 600 \pi \, \text{cm}
\]

Thus, the tip of the second hand travels a distance of \( 600\pi \) cm in one hour. If we approximate \( \pi \) as 3.14, it becomes:
\[
600 \pi \approx 600 \times 3.14 = 1884 \, \text{cm}
\]

In conclusion, the tip of the second hand travels **600π cm** or approximately **1884 cm** in one hour.