99 Percentile Qs Bank for JEE MainMathematicsApplication of Derivatives

The height of right circular cylinder of maximum volume inscribed in a sphere of diameter 2 a is

Options

A2 3 a
B3 a
C2 a 3
Da 3

Correct answer

C. 2 a 3

Step-by-step solution

Let the radius and height of the cylinder are and h , respectively. In A O M array l r²+ ( h² 4 )=a² h²=4 (a²-r² ) array Now, V= r² h= (a² h- 1 4 h³ ) For max or min, aligned & d V d h &= (a²- 3 4 h² )=0 & h &= ( 2 3 ) a aligned Now, d² V d h² =- 6 h 4 < 0 So, V is maximum at h= 2 a 3 .

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