A cone of maximum volume is inscribed in a sphere of radius R. The height of the cone is:

A cone of maximum volume is inscribed in a sphere of radius R. The height of the cone is:

• A. 4R/3
• B. 2R/3
• C. R/2
• D. 3R/4

Answer: A) 4R/3

Explanation: Let height = h, radius of base = r. From geometry, (h − R)² + r² = R² → r² = R² − (h − R)² = 2Rh − h². Volume V = (1/3)πr²h = (1/3)π(2Rh − h²)h = (π/3)(2Rh² − h³). dV/dh = (π/3)(4Rh − 3h²) = 0 → h(4R − 3h) = 0 → h = 4R/3.