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Ratio of the circumference and the diame...

Ratio of the circumference and the diameter of a circle is more than 3.

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To solve the problem of determining whether the ratio of the circumference to the diameter of a circle is more than 3, we can follow these steps: ### Step-by-Step Solution: 1. **Understand the Definitions**: - The **circumference** (C) of a circle is given by the formula: \[ C = 2\pi r \] where \( r \) is the radius of the circle. - The **diameter** (D) of a circle is given by the formula: \[ D = 2r \] 2. **Set Up the Ratio**: - We need to find the ratio of the circumference to the diameter: \[ \text{Ratio} = \frac{C}{D} \] 3. **Substitute the Formulas**: - Substitute the formulas for circumference and diameter into the ratio: \[ \text{Ratio} = \frac{2\pi r}{2r} \] 4. **Simplify the Ratio**: - The \( 2r \) in the numerator and denominator cancels out: \[ \text{Ratio} = \frac{2\pi r}{2r} = \pi \] 5. **Evaluate the Value of Pi**: - The value of \( \pi \) (pi) is approximately \( 3.14 \). 6. **Compare with 3**: - Since \( \pi \approx 3.14 \), we can conclude that: \[ \pi > 3 \] 7. **Conclusion**: - Therefore, the statement that the ratio of the circumference to the diameter of a circle is more than 3 is **true**.
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