# Rate of change

1. May 15, 2013

### whynot314

A=$\pi$$r^{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?

2. May 15, 2013

### Staff: Mentor

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

3. May 15, 2013

### 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?

4. May 15, 2013

### Staff: Mentor

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.

5. May 15, 2013

Thanks