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)
A 18.4 6.2 ?
B 25.1 8.0 ?
C 31.4 10.0 ?
D 40.0 12.9 ?
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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1 answer

To complete the table, we need to calculate the ratio of circumference (C) to diameter (d) for each cylinder. The ratio can be calculated using the formula:

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

We will calculate the ratio for each of the given cylinders and round to the nearest tenth.

Calculations:

  1. Cylinder A:

    • \( C = 18.4 , \text{cm}, , d = 6.2 , \text{cm} \) \[ \text{Ratio} = \frac{18.4}{6.2} \approx 2.965 \approx 3.0 \]
  2. Cylinder B:

    • \( C = 25.1 , \text{cm}, , d = 8.0 , \text{cm} \) \[ \text{Ratio} = \frac{25.1}{8.0} \approx 3.1375 \approx 3.1 \]
  3. Cylinder C:

    • \( C = 31.4 , \text{cm}, , d = 10.0 , \text{cm} \) \[ \text{Ratio} = \frac{31.4}{10.0} \approx 3.14 \approx 3.1 \]
  4. Cylinder D:

    • \( C = 40.0 , \text{cm}, , d = 12.9 , \text{cm} \) \[ \text{Ratio} = \frac{40.0}{12.9} \approx 3.1023 \approx 3.1 \]

Completed Table:

| Cylinder | Circumference, C (cm) | Diameter, d (cm) | Ratio | |----------|------------------------|-------------------|-------| | A | 18.4 | 6.2 | 3.0 | | B | 25.1 | 8.0 | 3.1 | | C | 31.4 | 10.0 | 3.1 | | D | 40.0 | 12.9 | 3.1 |

Conclusion:

To the nearest whole number, the circumference of the base of a cylinder is approximately 3 times the diameter of the same base.