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Average Rate of Change

The radius of...

Question

The radius of a circle is increasing at the rates of $0.7$ cm/sec. What is the rate of increasing of its circumference, when the radius of the circle is $4.9$ cm ?

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Solution

$Given \frac{d r}{d t} = 0.7 c m / s e c Perimeter P = 2 π r, where r = radius \frac{d P}{d t} = \frac{d}{d t} (2 π r) \Rightarrow \frac{d P}{d t} = 2 π \frac{d r}{d t}$
$\frac{d P}{d t} = 2 π \frac{(0.7) c m}{sec} \frac{d P}{d t} = \frac{7}{5} π c m / s e c$
it does not depend on radius of circle

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