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  • Help me please, - Limit , continuity and differentiability - JEE Main-9

The radius of a circle is increasing at 2 cm/sec then the rate of increase of its area when radius is \frac{1}{\pi} cm will be ?

  • Option 1)

    2 cm2 /sec

  • Option 2)

    4 cm2 /sec

  • Option 3)

    6 cm2 /sec

  • Option 4)

    8 cm2 /sec

 

Answers (1)

best_answer

As we have learned

Rate Measurement -

Rate of any of variable with respect to time is rate of measurement. Means according to small change in time how much other factors change is rate measurement:

\Rightarrow \frac{dx}{dt},\:\frac{dy}{dt},\:\frac{dR}{dt},(linear),\:\frac{da}{dt}


\Rightarrow \frac{dS}{dt},\:\frac{dA}{dt}(Area)


\Rightarrow \frac{dV}{dt}(Volume)


\Rightarrow \frac{dV}{V}\times 100(percentage\:change\:in\:volume)

- wherein

Where dR / dt  means Rate of change of radius.

 

 A=\pi r^{2}\Rightarrow \frac{dA}{dt} = 2\pi r\frac{dr}{dt}

\because \frac{dr}{dt}= 2 cm/ s

\because \frac{dA}{dt} ..at.. r= 1/\pi cm   will be \frac{dA}{dt}= 2\pi \times 1/\pi \times 2= 4cm^{2}/s 

 

 

 

 

 


Option 1)

2 cm2 /sec

Option 2)

4 cm2 /sec

Option 3)

6 cm2 /sec

Option 4)

8 cm2 /sec

Posted by

Himanshu

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