JEE Main 2019MathematicsApplication of DerivativesMediumMCQ

JEE Main 2019 — Application of Derivatives Question with Solution

JEE Main 2019 (08 Apr Shift 2)

Question

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

Choose an option

Show full solutionCorrect option: D
Correct answer
D2 3

Step-by-step explanation


From the diagram, we get radius of cylinder =R2-h22
⇒ Volume of cylinder V=πR2-h24h
For maximum volume: dVdh=0
⇒πR2-3h24=0
⇒h2=4R23=4×93=12
⇒h=23

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About this question

This is a previous-year question from JEE Main 2019, covering the Application of Derivatives chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.