PUC Karnataka Science Class 12Department of Pre-University Education, Karnataka
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In a Sphere the Rate of Change of Volume is (A) π Times the Rate of Change of Radius (B) Surface Area Times the Rate of Change of Diameter (C) Surface Area Times the Rate of Change of Radius - PUC Karnataka Science Class 12 - Mathematics

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Question

In a sphere the rate of change of volume is

  • π times the rate of change of radius

  • surface area times the rate of change of diameter

  •  surface area times the rate of change of radius

  • none of these

Solution

surface area times the rate of change of radius

\[\text { Let r be the radius andVbe the volume of sphere at any time t.Then },\]

\[V = \frac{4}{3}\pi r^3 \]

\[ \Rightarrow \frac{dV}{dt} = \frac{4}{3}\left( 3\pi r^2 \right)\left( \frac{dr}{dt} \right)\]

\[ \Rightarrow \frac{dV}{dt} = 4\pi r^2 \left( \frac{dr}{dt} \right)\]

\[\text { Thus, the rate of change of volume is surface area times the rate of change of the radius }.\]

  Is there an error in this question or solution?
Solution In a Sphere the Rate of Change of Volume is (A) π Times the Rate of Change of Radius (B) Surface Area Times the Rate of Change of Diameter (C) Surface Area Times the Rate of Change of Radius Concept: Rate of Change of Bodies Or Quantities.
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