Question:
Quantity A: The volume of a cylinder with radius 3 and height 4
Quantity B: 3 times the volume of a cone with radius 3 and height 4
Which of the following is true?
Quantity A: The volume of a cylinder with radius 3 and height 4
Quantity B: 3 times the volume of a cone with radius 3 and height 4
Which of the following is true?
Quantity B: 3 times the volume of a cone with radius 3 and height 4
Which of the following is true?
Show Hint
Cylinder volume = \(\pi r^2 h\), Cone volume = \(\tfrac{1}{3}\pi r^2 h\).
Updated On: Oct 3, 2025
- The relationship cannot be determined.
- The two quantities are equal.
- Quantity B is greater.
- Quantity A is greater.
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The Correct Option is B
Solution and Explanation
Step 1: Cylinder volume.
\[ V = \pi r^2 h = \pi (3^2)(4) = 36\pi \] Step 2: Cone volume.
\[ V = \tfrac{1}{3}\pi r^2 h = \tfrac{1}{3}\pi (9)(4) = 12\pi \] So 3 times cone volume = \(36\pi\).
Step 3: Compare.
Quantity A = \(36\pi\), Quantity B = \(36\pi\).
Final Answer: \[ \boxed{\text{The two quantities are equal}} \]
\[ V = \pi r^2 h = \pi (3^2)(4) = 36\pi \] Step 2: Cone volume.
\[ V = \tfrac{1}{3}\pi r^2 h = \tfrac{1}{3}\pi (9)(4) = 12\pi \] So 3 times cone volume = \(36\pi\).
Step 3: Compare.
Quantity A = \(36\pi\), Quantity B = \(36\pi\).
Final Answer: \[ \boxed{\text{The two quantities are equal}} \]
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