Question

Mrs. Amrich gave her students an activity to help them see the relationship between the circumference and diameter of a circle. Working together with a partner, the students had to wrap a piece of string around the outside of a circle, then measure its length to find the circumference of the circle. The students also had to use the string to measure the diameter of the circle.

Mrs. Amrich had each pair of students complete a data table and a conclusion statement. She explained that there was likely a little error in their measurements with the string, so the data really just showed the approximate ratio of the circumference of a circle to the diameter of the circle.

The data for one pair of students is shown below. Complete the table and the conclusion statement.



Circle Circumference, C Diameter, d Ratio:







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

Answer 1

Let's say the students wrapped the string around a circle and measured the following values:

- Circumference (C) = 31.4 cm
- Diameter (d) = 10 cm

Now, let's complete the data table based on these measurements:

| Circle | Circumference, C | Diameter, d | Ratio: |
|--------|------------------|--------------|-----------|
| 1 | 31.4 cm | 10 cm | 3.1 |

To find the ratio, we can use the formula:
\[ \text{Ratio} = \frac{C}{d} \]
\[ \text{Ratio} = \frac{31.4 \text{ cm}}{10 \text{ cm}} = 3.14 \]

Rounding this to the nearest tenth, we get 3.1.

Now, let's complete the conclusion statement:
Conclusion: To the nearest whole number, the circumference of a circle is **3** times the diameter of the circle.