Question:
A right circular cylinder of volume \(200\pi\) has a height of 8. Quantity A: 10. Quantity B: The circumference of the base.
A right circular cylinder of volume \(200\pi\) has a height of 8. Quantity A: 10. Quantity B: The circumference of the base.
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Cylinder formula: \(V = \pi r^2 h\), circumference = \(2\pi r\).
Updated On: Oct 3, 2025
- Quantity B is greater.
- The relationship cannot be determined.
- The two quantities are equal.
- Quantity A is greater.
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The Correct Option is C
Solution and Explanation
Step 1: Formula for volume of a cylinder.
\[ V = \pi r^2 h \] Given \(200\pi = \pi r^2 (8)\). Step 2: Solve for radius.
\[ r^2 = \frac{200}{8} = 25 \implies r = 5 \] Step 3: Circumference of base.
\[ C = 2\pi r = 2\pi(5) = 10\pi \] Step 4: Compare quantities.
Quantity A = 10.
Quantity B = \(10\pi \approx 31.4\).
So, Quantity B is actually greater (not equal).
Final Answer:
\[ \boxed{\text{Quantity B is greater}} \]
\[ V = \pi r^2 h \] Given \(200\pi = \pi r^2 (8)\). Step 2: Solve for radius.
\[ r^2 = \frac{200}{8} = 25 \implies r = 5 \] Step 3: Circumference of base.
\[ C = 2\pi r = 2\pi(5) = 10\pi \] Step 4: Compare quantities.
Quantity A = 10.
Quantity B = \(10\pi \approx 31.4\).
So, Quantity B is actually greater (not equal).
Final Answer:
\[ \boxed{\text{Quantity B is greater}} \]
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