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If radius of circle is creased by 1% then its area will b increased by 

  • Option 1)

    1/%

  • Option 2)

    1%

  • Option 3)

    2%

  • Option 4)

    3%

 

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 log _{e} A= log_{e}\pi + log _{e}r^{2}

\Rightarrow log _{e} A= log_{e}\pi + 2log _{e}r

Diffrentiating both sides , with respect to 'r' 

\Rightarrow 1/A\frac{dA}{dr}=0+2/r\Rightarrow \frac{dA}{A}=\frac{2dr}{r}

\Rightarrow \frac{dA}{A}\times 100=2\frac{2dr}{r}\times 100

Here \frac{dr}{r}\times 100= 1

so \frac{dA}{A}\times 100= 2*1=2

Area will be increased by 2 %

 

 

 

 

 


Option 1)

1/%

Option 2)

1%

Option 3)

2%

Option 4)

3%

Posted by

Himanshu

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