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.
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.
Answers
GPT-4o mini
To help complete the table and derive a conclusion, we first need to understand the relationship between the circumference (C) and diameter (d) of a cylinder, which is given by the formula:
\[ C = \pi \times d \]
The ratio of the circumference to the diameter is:
\[ \text{Ratio} = \frac{C}{d} = \pi \approx 3.14 \]
Now, we'll fill in the table based on typical data for the circumference and diameter of cylinders. Since you haven't provided specific measurements, I will assume some example data for three groups. You can replace these values with actual measurements as needed.
### Example Table:
| Cylinder | Circumference, C (cm) | Diameter, d (cm) | Ratio (C/d) |
|----------|------------------------|-------------------|-------------|
| Group 1 | 31.4 | 10 | 3.1 |
| Group 2 | 62.8 | 20 | 3.1 |
| Group 3 | 94.2 | 30 | 3.1 |
### Calculating the Ratios:
1. Group 1: \( \text{Ratio} = \frac{31.4}{10} = 3.14 \)
2. Group 2: \( \text{Ratio} = \frac{62.8}{20} = 3.14 \)
3. Group 3: \( \text{Ratio} = \frac{94.2}{30} = 3.14 \)
### Conclusion:
The ratios calculated reflect that:
- To the nearest whole number, the circumference of the base of a cylinder is approximately **3 times** the diameter of the same base.
Feel free to fill in the actual values you have for the cylinders, compute the ratios, and make the conclusion accordingly!
\[ C = \pi \times d \]
The ratio of the circumference to the diameter is:
\[ \text{Ratio} = \frac{C}{d} = \pi \approx 3.14 \]
Now, we'll fill in the table based on typical data for the circumference and diameter of cylinders. Since you haven't provided specific measurements, I will assume some example data for three groups. You can replace these values with actual measurements as needed.
### Example Table:
| Cylinder | Circumference, C (cm) | Diameter, d (cm) | Ratio (C/d) |
|----------|------------------------|-------------------|-------------|
| Group 1 | 31.4 | 10 | 3.1 |
| Group 2 | 62.8 | 20 | 3.1 |
| Group 3 | 94.2 | 30 | 3.1 |
### Calculating the Ratios:
1. Group 1: \( \text{Ratio} = \frac{31.4}{10} = 3.14 \)
2. Group 2: \( \text{Ratio} = \frac{62.8}{20} = 3.14 \)
3. Group 3: \( \text{Ratio} = \frac{94.2}{30} = 3.14 \)
### Conclusion:
The ratios calculated reflect that:
- To the nearest whole number, the circumference of the base of a cylinder is approximately **3 times** the diameter of the same base.
Feel free to fill in the actual values you have for the cylinders, compute the ratios, and make the conclusion accordingly!