Question:
Quantity A: The diameter of a circle with area of \( 109\pi \)
Quantity B: The diameter of a circle with circumference of \( 22\pi \)
Which of the following is true?
Quantity A: The diameter of a circle with area of \( 109\pi \)
Quantity B: The diameter of a circle with circumference of \( 22\pi \)
Which of the following is true?
Quantity B: The diameter of a circle with circumference of \( 22\pi \)
Which of the following is true?
Show Hint
When comparing circle properties, always express diameter in terms of given area or circumference.
Updated On: Oct 3, 2025
- Quantity B is larger.
- The relationship between the quantities cannot be determined.
- Quantity A is larger.
- The two quantities are equal.
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The Correct Option is C
Solution and Explanation
Step 1: Diameter from area.
\[ \pi r^2 = 109\pi \quad \Rightarrow \quad r^2 = 109 \quad \Rightarrow \quad r = \sqrt{109} \] So diameter \( D_A = 2\sqrt{109} \).
Step 2: Diameter from circumference.
\[ C = 22\pi \quad \Rightarrow \quad 2\pi r = 22\pi \quad \Rightarrow \quad r = 11 \] So diameter \( D_B = 22 \).
Step 3: Compare diameters.
Since \( 2\sqrt{109} \approx 20.88<22 \), actually **Quantity B is larger**.
Final Answer: \[ \boxed{\text{Quantity B is larger}} \]
\[ \pi r^2 = 109\pi \quad \Rightarrow \quad r^2 = 109 \quad \Rightarrow \quad r = \sqrt{109} \] So diameter \( D_A = 2\sqrt{109} \).
Step 2: Diameter from circumference.
\[ C = 22\pi \quad \Rightarrow \quad 2\pi r = 22\pi \quad \Rightarrow \quad r = 11 \] So diameter \( D_B = 22 \).
Step 3: Compare diameters.
Since \( 2\sqrt{109} \approx 20.88<22 \), actually **Quantity B is larger**.
Final Answer: \[ \boxed{\text{Quantity B is larger}} \]
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