Question:

O is the center of the circle with radius 6.
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To calculate the length of an arc, use the formula \( \text{Arc length} = 2\pi r \times \frac{\theta}{360} \), where \( r \) is the radius and \( \theta \) is the central angle.
Updated On: Sep 30, 2025
  • The quantity in Column A is greater.
  • The quantity in Column B is greater.
  • The two quantities are equal.
  • The relationship cannot be determined from the information given.
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The Correct Option is D

Solution and Explanation

Step 1: Using the formula for the length of an arc.
The length of an arc is given by the formula: \[ \text{Arc length} = 2\pi r \times \frac{\theta}{360} \] Where \( r = 6 \) (radius) and \( \theta = 60^\circ \) (the angle at the center). Substituting these values into the formula: \[ \text{Arc length} = 2\pi (6) \times \frac{60}{360} = \pi (6) \times \frac{1}{6} = \pi \approx 3.14 \]
This gives an arc length of approximately \( 3.14 \), while Column B is 6.
Step 2: Conclusion.
Since \( 3.14 \neq 6 \), the quantities in Column A and Column B are not equal, and the relationship cannot be determined from the given information.
Final Answer: \[ \boxed{\text{The relationship cannot be determined from the information given.}} \]
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