The height of a right circular cylinder of maximum volume inscribed in a sphere of radius 3 is

Correct option is A. 2√3
Step - 1: First find height and area and the substitute in the formula of volume
h = rsinθ + rsinθ = 2rsinθ
a = 2rcosθ
v = π(rcosθ)²(2rsinθ)
v = 2πr³cos²θsinθ
Step - 2: Take the derivative of volume with respect to θ
dv/dθ = πr³(-2cosθsin²θ + cos³θ) = 0
tan²θ = 1/2
h = 2 × 3 × 1/√3 = 2√3
Thus, the height is 2√3