Geometry and TrigonometryVery hardSurface area of a sphere from its volume
Geometry and Trigonometry practice question
A sphere has a volume of 36π. What is its surface area? (For a sphere of radius r, the volume is (4/3)πr³ and the surface area is 4πr².)
- A. 36πCorrect
- B. 12π
- C. 9π
- D. 108π
Answer: A. 36π
(4/3)πr³ = 36π gives r³ = 27, so r = 3. Surface area = 4π(3²) = 36π.
Why the other answers are wrong
- B. 12π
- 12π is 4π × 3, using r instead of r².
- C. 9π
- 9π is πr², a great-circle area, not the sphere's surface.
- D. 108π
- 108π is 4π × 27, using r³ instead of r².
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