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Question
The radius of a sphere is changing at the rate of 0.1 cm/sec. The rate of change of its surface area when the radius is 200 cm is
Options
8π cm2/sec
12π cm2/sec
160π cm2/sec
200 cm2/sec
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Solution
160π cm2/sec
\[\text { Let r be the radius and S be the surface area of the sphere at any time t.Then },\]
\[S = 4\pi r^2 \]
\[\Rightarrow\frac{dS}{dt}=8\pi r\frac{dr}{dt}\]
\[\Rightarrow\frac{dS}{dt}=8\pi\left( 200 \right)\left( 0 . 1 \right)\]
\[\Rightarrow\frac{dS}{dt} {=160\pi \ cm}^2 /sec\]
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