Question

related rates
A stone is dropped into a calm body of water, causing ripples in the form of concentric circles. The radius of the outer ripple is increasing at a rate of 1 foot per second. When the radius is 4 feet, at what rate is the total area of the disturbed water changing?

Answer 1

I used \[A=\pi r^2\]

Answer 2

\[\frac{ dA }{ dt }=2\pi r \frac{ dr }{ dt }\]

Answer 3

I got \[\frac{ dA }{ dt}=8 \pi \]

Answer 4

units are ft^2/sec

Answer 5

Yes, that is correct.

Answer 6

thanks, I actually have one that I am stuck on but I am going to close this one out and post it by itself. Do you can help me with it?

Answer 7

We will see.

Answer 8

thanks