rate of change

[jon12]

A stone is tossed into a calm pond and a circular ripple it creates has a radius that is increasing at a rate of 4 centimeters per second. Find the rate of change of the area when the radius of the circle is 24 centimeters.

 

[Deleted member 4993]

A stone is tossed into a calm pond and a circular ripple it creates has a radius that is increasing at a rate of 4 centimeters per second. Find the rate of change of the area when the radius of the circle is 24 centimeters.

Please show us your work, indicating exactly where you are stuck - so that we may know where to begin to help you.

 

[galactus]

Use the area of a circle formula:

\(\displaystyle A={\pi}r^{2}\)

Now, differentiate implicitly w.r.t r (in short, differentiate and attach a dr/dt), sub in your given dr/dt value, and you're finished.