JEE Main 2012 — Application Of Derivatives Question with Solution
From: AIEEE 2012
Question
A spherical balloon is filled with cubic meters of helium gas. If a leak in the balloon causes the gas to escape at the rate of cubic meters per minute, then the rate (in meters per minute) at which the radius of the balloon decreases minutes after the leakage began is :
Choose an option
Show full solutionCorrect option: C
Correct answer
C
Step-by-step explanation
Volume of spherical balloon
( as Given, volume )
Differentiating both the sides, we get,
Now, it is given that
After min, Volume -
Also, we have
( as Given, volume )
Differentiating both the sides, we get,
Now, it is given that
After min, Volume -
Also, we have
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This is a previous-year question from JEE Main 2012, 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.