Geometry and TrigonometryHardCylinder volume from its base circumference
Geometry and Trigonometry practice question
The base of a right circular cylinder has a circumference of 12π, and the cylinder has a height of 5. What is the volume of the cylinder?
- A. 180πCorrect
- B. 60π
- C. 720π
- D. 30π
Answer: A. 180π
Circumference 2πr = 12π gives r = 6. Volume = πr²h = π(36)(5) = 180π.
Why the other answers are wrong
- B. 60π
- 60π is π × 12 × 5, using the circumference number in place of r². The radius is 6 and r² = 36.
- C. 720π
- 720π squares the diameter (12² = 144) instead of the radius: 144 × 5 = 720. r = 6.
- D. 30π
- 30π is π × 6 × 5, forgetting to square the radius.
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