Question

Mr. Johnson's physics class is investigating the relationship between the circumference and diameter of the bases of the cylinders. Each group rolls a cylinder of different dimensions along a straight line and measures the distance it travels in one full rotation (circumference) and its diameter. The data for three groups is shown below. Complete the table below:


cylinder Circumference, C (cm) Diameter, d (cm) Ratio:







(Round to the nearest tenth)
Conclusion: To the nearest whole number, the circumference of the base of a cylinder is
times the diameter of the same base.

Answer 1

To calculate the ratio of circumference (C) to diameter (d) for each cylinder, you can use the formula:

\[
\text{Ratio} = \frac{C}{d}
\]

Let’s assume the data for the three groups is as follows:

- Group 1: C = 31.4 cm, d = 10 cm
- Group 2: C = 62.8 cm, d = 20 cm
- Group 3: C = 94.2 cm, d = 30 cm

Now, let's fill in the table and calculate each ratio.

### Calculations:
1. **Group 1:**
- C = 31.4 cm
- d = 10 cm
- Ratio = \( \frac{31.4}{10} = 3.14 \)

2. **Group 2:**
- C = 62.8 cm
- d = 20 cm
- Ratio = \( \frac{62.8}{20} = 3.14 \)

3. **Group 3:**
- C = 94.2 cm
- d = 30 cm
- Ratio = \( \frac{94.2}{30} = 3.14 \)

### Filling the Table:

| Cylinder | Circumference, C (cm) | Diameter, d (cm) | Ratio |
|----------|-----------------------|------------------|---------|
| Group 1 | 31.4 | 10 | 3.1 |
| Group 2 | 62.8 | 20 | 3.1 |
| Group 3 | 94.2 | 30 | 3.1 |

### Conclusion:
To the nearest whole number, the circumference of the base of a cylinder is **3** times the diameter of the same base.