Is Changing Radius Constant Equal to a Constant Rate of Change in Area?

[whynot314]

A=\pir^{2}

therfore,

\frac{dA}{dt}=2\pi\frac{dr}{dt}

The question is if \frac{dr}{dt} is constant is \frac{dA}{dt} constant?

To me, I know that if the change in radius with respect to time is constant, The rate of change of the are with respect to time still depends on the radius of the circle at some time. Therefore dA/dt is not constant.

Is this right?

Also am I wording this correctly?

 

[Mark44]

A=\pir^{2}

therfore,

\frac{dA}{dt}=2\pi\frac{dr}{dt}

No.
$$ \frac{dA}{dt} =2\pi r \frac{dr}{dt}$$

The question is if \frac{dr}{dt} is constant is \frac{dA}{dt} constant?

Does what I wrote answer your question?

To me, I know that if the change in radius with respect to time is constant, The rate of change of the are with respect to time still depends on the radius of the circle at some time. Therefore dA/dt is not constant.

Is this right?

Also am I wording this correctly?

 

[whynot314]

whoops yea forgot the r there, That was the r I was talking about in my answer. so what I said still applies right?

 

[Mark44]

Right, dA/dt is not constant. Even if r increases at a constant rate (i.e., dr/dt is constant), dA/dt does not change at a constant rate.

 

[whynot314]

Thanks