JEE Main20198 Apr 2019Evening ShiftMathematicsApplication of DerivativesActual

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

Options

A3
B2 3 3
C6
D2 3

Correct answer

D. 2 3

Step-by-step solution

From the diagram, we get radius of cylinder = R 2 - h 2 2 ⇒ Volume of cylinder V = π R 2 - h 2 4 h For maximum volume: d V d h = 0 ⇒ π R 2 - 3 h 2 4 = 0 ⇒ h 2 = 4 R 2 3 = 4 × 9 3 = 12 ⇒ h = 2 3

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