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प्रश्न
In a sphere the rate of change of surface area is
विकल्प
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
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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