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Question
The radius of a circular plate is increasing at the rate of 0.01 cm/sec. The rate of increase of its area when the radius is 12 cm, is
Options
144 π cm2/sec
2.4 π cm2/sec
0.24 π cm2/sec
0.024 π cm2/sec
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Solution
0.24 π cm2/sec
\[\text { Let r be the radius and A be the area of the circular plate at any timet.Then,} \]
\[A=\pi r^2 \]
\[\Rightarrow\frac{dA}{dt}=2\pi r\frac{dr}{dt}\]
\[\Rightarrow\frac{dA}{dt}=2\pi\left( 12 \right)\left( 0 . 01 \right)\]
\[\Rightarrow\frac{dA}{dt} {=0.24\pi \ cm}^2 /sec\]
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