#### 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.