JEE Main 2014 — Application of Derivatives Question with Solution
JEE Main 2014 (11 Apr Online)
Question
The volume of the largest possible right circular cylinder that can be inscribed in a sphere of radius is:
Choose an option
Show full solutionCorrect option: C
Correct answer
C
Step-by-step explanation
Given, radius of sphere
Now, In , by Pythagoras theorem
Now, volume of cylinder Now, for largest possible right circular cylinder the volume must be maximum For maximum volume, Now, Differentiating eq. (2) w.r.t. or Now, volume of the cylinder
Now, volume of cylinder Now, for largest possible right circular cylinder the volume must be maximum For maximum volume, Now, Differentiating eq. (2) w.r.t. or Now, volume of the cylinder
Practice this on the real CBT interface
Solve this JEE Main question (and the rest of the Application of Derivatives chapter) on PrepSharp's TCS iON-style CBT player — with timer, bookmarks and session analytics.
Solve interactively →About this question
This is a previous-year question from JEE Main 2014, 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.