Geometry and TrigonometryVery hardSurface area of a sphere from its volume
Geometry and Trigonometry practice question
A sphere has a volume of 36π cubic units. What is its surface area?
- A. 36πCorrect
- B. 12π
- C. 9π
- D. 108π
Answer: A. 36π
(4/3)πr³ = 36π gives r³ = 27, so r = 3 and the surface area is 4π(3)² = 36π.
Why the other answers are wrong
- B. 12π
- This uses 4πr instead of 4πr².
- C. 9π
- This is πr², one great circle.
- D. 108π
- This multiplies the volume by 3.
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