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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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