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In a Sphere the Rate of Change of Surface Area is (A) 8π Times the Rate of Change of Diameter (B) 2π Times the Rate of Change of Diameter (C) 2π Times the Rate of Change of Radius - Mathematics

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Question

In a sphere the rate of change of surface area is

Options
  • 8π times the rate of change of diameter

  • 2π times the rate of change of diameter

  • 2π times the rate of change of radius

  • 8π times the rate of change of radius

Solution

 8π times the rate of change of radius

\[\text { Let r be the radius and S be the surface area of the sphere at any time t .Then },\]

\[S = 4\pi r^2 \]

\[ \Rightarrow \frac{dS}{dt} = 8\pi r\frac{dr}{dt}\]

\[ \therefore \text { The rate of change of surface area is } 8\pi \text { times the rate of change of the radius.}\]

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APPEARS IN

 RD Sharma Solution for Mathematics for Class 12 (Set of 2 Volume) (2018 (Latest))
Chapter 13: Derivative as a Rate Measurer
Q: 25 | Page no. 26
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In a Sphere the Rate of Change of Surface Area is (A) 8π Times the Rate of Change of Diameter (B) 2π Times the Rate of Change of Diameter (C) 2π Times the Rate of Change of Radius Concept: Rate of Change of Bodies Or Quantities.
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