# Math Help - Rate of Change problem

1. ## Rate of Change problem

A stone is dropped into a lake, creating a circular ripple that travels outward at a speed of 60 cm/s. Find the rate at which the area within the circle is increasing after 3 seconds.

What do I do? I think I am supposed to use the formula of the area of a circle, but I am not sure how to use it.

2. Originally Posted by Maziana
A stone is dropped into a lake, creating a circular ripple that travels outward at a speed of 60 cm/s. Find the rate at which the area within the circle is increasing after 3 seconds.

What do I do? I think I am supposed to use the formula of the area of a circle, but I am not sure how to use it.
take the time derivative of the area equation ...

$\frac{d}{dt}[A = \pi r^2]
$

... then use the given info to determine $\frac{dA}{dt}$

3. I don't understand what I do to get rid of the r and plug in s...

4. Originally Posted by Maziana
I don't understand what I do to get rid of the r and plug in s...
what do you mean by "s" ?

5. Seconds, which is 3 in this problem.

6. Originally Posted by Maziana
Seconds, which is 3 in this problem.
you only need the 3 sec to determine the size of the radius which is increasing at 60 cm per second.

$\frac{dA}{dt} = 2\pi r \cdot \frac{dr}{dt}$

$\frac{dA}{dt} = 2\pi (180 \, cm) \cdot (60 \, cm/s)$