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Question
The radius of a circle is increasing at the rate of 0.5 cm/sec. Find the rate of increase of its circumference ?
Solution
\[\text { Let r be the radius and C be the circumference of the circle at any time t.Then,}\]
\[C = 2\pi r\]
\[ \Rightarrow \frac{dC}{dt} = 2\pi\frac{dr}{dt}\]
\[ \Rightarrow \frac{dC}{dt} = 2\pi \times 0 . 5 \left[ \because\frac{dr}{dt}=0.5 cm/sec \right]\]
\[ \Rightarrow \frac{dC}{dt} = \pi cm/\sec\]
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