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:

Question

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








c/d (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.
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Answer 1

To find the ratios and complete the table for the three cylinders, we will use the formula for the ratio of circumference (C) to diameter (d), which is \( \frac{C}{d} \).

Here's the process:

Given Data for Each Cylinder

Let's assume the following arbitrary measurements for circumference (C) and diameter (d) for three different cylinders, as you haven't provided specific values.

1. Cylinder 1: C = 31.4 cm, d = 10 cm
2. Cylinder 2: C = 62.8 cm, d = 20 cm
3. Cylinder 3: C = 15.7 cm, d = 5 cm

Calculation of Ratio (C/d)

• For Cylinder 1: \[ \text{Ratio} = \frac{31.4}{10} = 3.14 \quad (\text{rounded to } 3.1) \]

• For Cylinder 2: \[ \text{Ratio} = \frac{62.8}{20} = 3.14 \quad (\text{rounded to } 3.1) \]

• For Cylinder 3: \[ \text{Ratio} = \frac{15.7}{5} = 3.14 \quad (\text{rounded to } 3.1) \]

Filled Table

| Cylinder | Circumference, C (cm) | Diameter, d (cm) | Ratio: c/d | |------------|------------------------|-------------------|------------| | Cylinder 1 | 31.4 | 10 | 3.1 | | Cylinder 2 | 62.8 | 20 | 3.1 | | Cylinder 3 | 15.7 | 5 | 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.