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  • The radius of a circle is increasing at the rate of 0.7 cm/s. What is the rate of increase of its circumference?

The radius of a circle is increasing at the rate of 0.7 cm/s. What is the rate of increase of its circumference?

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Given =  \frac{dr}{dt} = 0.7 \ cm/s
To find =   \frac{dC}{dt}            , where C is circumference
Solution :-
 
we know that the circumference of the circle (C) = 2\pi r
\frac{dC}{dt} = \frac{dC}{dr}.\frac{dr}{dt}                              (by chain rule)
\frac{dC}{dt} = \frac{d2\pi r}{dr}.\frac{dr}{dt} = 2\pi \times 0.7 = 1.4\pi \ cm/s
Hence,  the rate of increase of its circumference is 1.4\pi \ cm/s

Posted by

Gautam harsolia

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