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)18.4 25.1 31.4 40.0 Diameter, d (cm)6.2 8.0 10.0 12.9 Ratio: c/d (Round to the nearest tenth) 3.1
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 complete the table and draw a conclusion based on the provided data, we will calculate the ratio of circumference to diameter (C/d) for each group of cylinders and round it to the nearest tenth.

The given data is:

| Cylinder | Circumference, C (cm) | Diameter, d (cm) | Ratio: C/d |
|----------|-----------------------|-------------------|------------|
| 1 | 18.4 | 6.2 | ? |
| 2 | 25.1 | 8.0 | ? |
| 3 | 31.4 | 10.0 | ? |
| 4 | 40.0 | 12.9 | ? |

Now, let's calculate the ratios:

1. For the first cylinder:
\[
\text{Ratio} = \frac{C}{d} = \frac{18.4}{6.2} \approx 2.9677 \approx 3.0 \, \text{(rounded to the nearest tenth)}
\]

2. For the second cylinder:
\[
\text{Ratio} = \frac{C}{d} = \frac{25.1}{8.0} \approx 3.1375 \approx 3.1 \, \text{(rounded to the nearest tenth)}
\]

3. For the third cylinder:
\[
\text{Ratio} = \frac{C}{d} = \frac{31.4}{10.0} = 3.14 \approx 3.1 \, \text{(rounded to the nearest tenth)}
\]

4. For the fourth cylinder:
\[
\text{Ratio} = \frac{C}{d} = \frac{40.0}{12.9} \approx 3.1008 \approx 3.1 \, \text{(rounded to the nearest tenth)}
\]

Now, let's fill in the table:

| Cylinder | Circumference, C (cm) | Diameter, d (cm) | Ratio: C/d |
|----------|-----------------------|-------------------|------------|
| 1 | 18.4 | 6.2 | 3.0 |
| 2 | 25.1 | 8.0 | 3.1 |
| 3 | 31.4 | 10.0 | 3.1 |
| 4 | 40.0 | 12.9 | 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.