The radius of a circle is increasing at 0.7 cm/sec. What is the rate of increase of its circumference when r = 4.9 cm?

Solution

Let C be the circumference of the circle whose radius is r at any time t.
$therefore space space space space straight C space equals space 2 space straight pi space straight r space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space rightwards double arrow space space dC over dt space equals space 2 straight pi dr over dt But space space space dr over dt space equals space 0.7 space cm divided by sec space space space space space space space space space space space space space rightwards double arrow space space space space dC over dt space equals space 2 straight pi space cross times space 0.7 space equals space 1.4 space straight pi therefore space space space rate space of space increase space of space circumference space space equals space 1.4 space straight pi space cm divided by sec. When space straight r space equals space 49 space cm comma space space space rate space of space increase space of space circumference space equals space 1.4 space straight pi space cm divided by sec$

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Application Of Derivatives

The radius of a circle is increasing at 0.7 cm/sec. What is the rate of increase of its circumference when r = 4.9 cm?

Some More Questions From Application of Derivatives Chapter

The radius of a circle is increasing uniformly at the rate of 4 cm per second Find the rate at which the area of the circle is increasing when the radius is 8 cm.

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