# Rate of Change problem

• Oct 5th 2009, 03:37 PM
Maziana
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.
• Oct 5th 2009, 04:23 PM
skeeter
Quote:

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 ...

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

... then use the given info to determine $\displaystyle \frac{dA}{dt}$
• Oct 5th 2009, 04:53 PM
Maziana
I don't understand what I do to get rid of the r and plug in s...
• Oct 5th 2009, 04:54 PM
skeeter
Quote:

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" ?
• Oct 5th 2009, 04:58 PM
Maziana
Seconds, which is 3 in this problem.
• Oct 5th 2009, 05:04 PM
skeeter
Quote:

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.

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

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