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  • If the radius of a circle is increasing at a uniform rate of 2 cm/s , find the rate of increase of area of circle , at the instant When the radius is 20 cm.

If the radius of a circle is increasing at a uniform rate of 2 cm/s , find the rate of increase of area of circle , at the instant When the radius is 20 cm.

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Solution: Given ,    fracmathrmd rmathrmd t=2cm/s        (where r radius andt time )

          Now, area of circle is given by A=pi r^2

  Diffrentiating it with respect to time t , we get

              \Rightarrow            fracmathrmd Amathrmd t=2pi rfracmathrmd rmathrmd t

             \Rightarrow         fracmathrmd Amathrmd t=2pi cdot 20cdot 2hspace0.2cmcm^2/s

                             fracmathrmd Amathrmd t= 80pi hspace0.1cmcm^2/s

Thus , the rate of change of Area of cicle with respect to time is 80pi hspace0.1cmcm^2/s.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Posted by

Deependra Verma

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