JEE Main 2020MathematicsApplication of DerivativesMediumMCQ

JEE Main 2020 — Application of Derivatives Question with Solution

JEE Main 2020 (03 Sep Shift 2)

Question

If the surface area of a cube is increasing at a rate of 3.6cm2/sec, retaining its shape; then the rate of change of its volume (in cm3/sec), when the length of a side of the cube is 10cm, is:

Choose an option

Show full solutionCorrect option: D
Correct answer
D9

Step-by-step explanation

Surface area of cube s=6a2

⇒dsdt=12adadt=3.6

⇒1210dadt=3.6⇒dadt=0.03cm/sec

Now, volume of cube V=a3

⇒dvdt=3a2.dadt=3(10)20.03=9cm3/sec

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About this question

This is a previous-year question from JEE Main 2020, 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.