JEE Main 2014MathematicsApplication of DerivativesMediumMCQ

JEE Main 2014 — Application of Derivatives Question with Solution

JEE Main 2014 (19 Apr Online)

Question

If the volume of a spherical ball is increasing at the rate of 4π cc/sec then the rate of increase of its radius in cm/sec, when the volume is 288π cc is 

Choose an option

Show full solutionCorrect option: D
Correct answer
D 1 3 6

Step-by-step explanation

Volume of sphere of radius r is V=43πr3

Given V=288π cc

⇒288π=43πr3

⇒r3=288×34=216

⇒r=6 cm.

Again, V=43πr3

Differentiate w.r.t. 't'

⇒dVdt=4πr2drdt

Put the given values, to get

⇒4π=4π×62×drdt

⇒drdt=136 cm/sec.

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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.