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प्रश्न
In a sphere the rate of change of surface area is
पर्याय
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
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उत्तर
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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