# stone problem

• Feb 27th 2010, 03:59 PM
slapmaxwell1
stone problem
a stone dropped into a still pond sends out a circular ripple whose radius increases at a constant rate of 3 ft/s. how rapidly is the area enclosed by the ripple increasing at the end of 10s? ok im not sure how to set this up? would it be A = pi(r)^2 so i take the derivative with respect to r? right? i got 1960 pi as an answer..
• Feb 27th 2010, 04:16 PM
skeeter
Quote:

Originally Posted by slapmaxwell1
a stone dropped into a still pond sends out a circular ripple whose radius increases at a constant rate of 3 ft/s. how rapidly is the area enclosed by the ripple increasing at the end of 10s? ok im not sure how to set this up? would it be A = pi(r)^2 so i take the derivative with respect to r? right? i got 1960 pi as an answer..

this is a related rates problem. you were given $\displaystyle \frac{dr}{dt} = 3$ ft/s
take the derivative of $\displaystyle A$ w/r to time, $\displaystyle t$ , and calculate the value of $\displaystyle \frac{dA}{dt}$ when r = 30 ft