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Question
The radius of a circle is increasing at the rate of 0.7 cm/sec. What is the rate of increase of its circumference?
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Solution
\[\text { Let r be the radius and C be the circumference of the circle at any time t.Then },\]
\[C = 2\pi r\]
\[ \Rightarrow \frac{dC}{dt} = 2\pi\frac{dr}{dt}\]
\[ \Rightarrow \frac{dC}{dt} = 2\pi \times 0 . 7 \left[ \because\frac{dr}{dt}=0.7 cm/sec \right]\]
\[ \Rightarrow \frac{dC}{dt} = 1 . 4\pi cm/\sec\]
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