A cylinder of circumference 8 cm and length 21 cm rolls without sliding for `4 (1)/(2) ` seconds at the rate of 9 complete rounds per second. Find :
the distance travelled by the cylinder in `4 (1)/(2)` seconds ?

Answer

To solve the problem step by step, we will follow the reasoning outlined in the video transcript.

### Step-by-Step Solution:

1. **Identify the Given Information:**
- Circumference of the cylinder = 8 cm
- Length of the cylinder = 21 cm (not needed for this calculation)
- Time = 4.5 seconds
- Rate of rotation = 9 complete rounds per second

2. **Calculate the Total Number of Rounds in 4.5 Seconds:**
\[ \text{Total rounds} = \text{Rate of rotation} \times \text{Time} = 9 \, \text{rounds/second} \times 4.5 \, \text{seconds} = 40.5 \, \text{rounds} \]

3. **Calculate the Distance Travelled in One Round:**
- The distance travelled in one complete round is equal to the circumference of the cylinder.
\[ \text{Distance in one round} = \text{Circumference} = 8 \, \text{cm} \]

4. **Calculate the Total Distance Travelled in 4.5 Seconds:**
\[ \text{Total distance} = \text{Total rounds} \times \text{Distance in one round} = 40.5 \, \text{rounds} \times 8 \, \text{cm} = 324 \, \text{cm} \]

5. **Final Answer:**
The distance travelled by the cylinder in 4.5 seconds is **324 cm**.