Geometry and TrigonometryVery hardVolume of a cone
Geometry and Trigonometry practice question
A cone has a radius of 6 and a height of 10. What is its volume? (Use V = (1/3)πr²h.)
- A. 120πCorrect
- B. 360π
- C. 60π
- D. 1080π
Answer: A. 120π
V = (1/3)π(6²)(10) = (1/3)π(36)(10) = (1/3)(360π) = 120π. Choice B (360π) forgets the 1/3 factor — that is the volume of the full cylinder, and a cone is exactly one-third of it.
Why the other answers are wrong
- B. 360π
- 360π is π(6²)(10), the volume of the full cylinder — you left out the 1/3 factor that makes it a cone.
- C. 60π
- 60π is π(6)(10), the radius times the height; the formula needs r² = 36, and then the 1/3 factor.
- D. 1080π
- 1080π comes from multiplying 360π by 3 instead of dividing by 3 — the formula has a factor of 1/3.
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