Related rates: When t is given and r is not

Homework Statement

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 10 s?

Homework Equations

How do I even set up implicit differentiation?

The Attempt at a Solution

I know that dr/dt is 3 ft/s and that I'm looking for dA/dt, but I don't know where t = 10s goes into that equation, especially when I don't have the radius... Do I multiply time times dr/dt to get radius at 10 seconds and go from there?

HELP!!

Last edited:

hage567
Homework Helper
Start with the formula for the area of a circle. You are given how the radius changes with time. Do you see how those might fit together to get an expression for the change in area? Start there and see if that helps you out.

Edit: Yes, you can get the radius at 10 seconds that way.

well, i know that dA/dt = 2pi*radius*dr/dt, but I don't have the radius...

hage567
Homework Helper
At 10 seconds you do. Actually at any second you do.

Sweetness.... Thanks so much! I've been going back and forth thinking that was just too easy. All the problems on this take home quiz have that one extra step you have to go thru to get all the info. It's making me crazy!

hage567
Homework Helper
It's making me crazy!

Yeah, calculus can do that to you. LOL