# Homework Help: Related RateArea of Circle

1. Jan 3, 2012

### Wa1337

1. The problem statement, all variables and given/known data
A stone dropped into a still pond sends out a circular ripple whose radius increases at a constant rate of 3 ft/s. Does the area also increase at a constant rate?

2. Relevant equations
A = ∏r2

3. The attempt at a solution
dA/dt = 2∏r(dr/dt)
dA/dt = 2∏r(3ft/s)

What now?

2. Jan 3, 2012

### Staff: Mentor

Now you answer the question - Is the area increasing at a constant rate?

3. Jan 3, 2012

### Wa1337

I mean, I guess it would, but I don't really know how to explain it.

4. Jan 3, 2012

### Staff: Mentor

The radius is increasing at a constant rate, since dr/dt = 3 (ft/sec).

The rate of change of the area is dA/dt = 6$\pi$r (ft2/sec). Does that look like a constant to you?

5. Jan 3, 2012

Yes.

6. Jan 3, 2012

### Staff: Mentor

A constant value shouldn't have a variable in it. The value of dA/dt depends on how big the circle is - IOW, dA/dt is NOT constant.

7. Jan 3, 2012

### Wa1337

Ok thanks I was very confused on this but you helped.