JEE Main 2019MathematicsApplication of DerivativesHardMCQ

JEE Main 2019 — Application of Derivatives Question with Solution

JEE Main 2019 (09 Jan Shift 1)

Question

The maximum volume in cu.m of the right circular cone having slant height 3 m is:

Choose an option

Show full solutionCorrect option: A
Correct answer
A23 π

Step-by-step explanation

Given l=3



⇒r2+h2=l2=9

Volume, V=13πr2h

⇒V=13π9-h2h=13π9h-h3

dvdh=13π9-3h2

dvdh=0⇒h=3

d2Vdh2=13π-6h<0

∴ at h=3 , cone has maximum volume

∴ Vmax=13π93-33=23πcm3

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 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.