A right circular cylinder is inscribed in a sphere of radius 3 cm. The maximum volume of the cylinder is:
A right circular cylinder is inscribed in a sphere of radius 3 cm. The maximum volume of the cylinder is:
- A. 12√3 π cm³
- B. 9√3 π cm³
- C. 6√3 π cm³
- D. 18√3 π cm³
Answer: A) 12√3 π cm³
Explanation: Let radius = r, height = 2h. r² + h² = 9. V = πr²(2h) = 2π(9 − h²)h = 2π(9h − h³). dV/dh = 2π(9 − 3h²) = 0 → h = √3. V = 2π(9√3 − 3√3) = 12√3 π.
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