If $V=4\pi r^3/3,$ at what rate in cubic

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Target Exam

CUET

Subject

-- Mathematics - Section A

Chapter

Applications of Derivatives

Question:

If $V=4\pi r^3/3,$ at what rate in cubic units/ sec is V increasing when r= 10, and dr/dt=0.01 ?

Options:

$\pi $

$4\pi $

$40\pi $

$4\pi /3 $

Correct Answer:

$4\pi $

Explanation:

The correct answer is Option (2) → $4\pi$

$\frac{dv}{dt}=4πr^2\frac{dr}{dt}$

$⇒4π(10)^2×0.01$

$=4π$