Geometry and TrigonometryHardVolume of a hemisphere
Geometry and Trigonometry practice question
A solid hemisphere has a radius of 3. What is its volume? (The volume of a sphere of radius r is (4/3)πr³.)
- A. 18πCorrect
- B. 36π
- C. 9π
- D. 12π
Answer: A. 18π
A full sphere of radius 3 has volume (4/3)π(27) = 36π. A hemisphere is half of that: 18π.
Why the other answers are wrong
- B. 36π
- 36π is the volume of the whole sphere; a hemisphere is half.
- C. 9π
- 9π is πr², the area of the flat circular face, not a volume.
- D. 12π
- 12π is (4/3)π × 9, using r² instead of r³.
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