Constant Rate of Change in Area of Circle with Changing Radius?

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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. Does the area also increase at a constant rate?


Homework Equations


A = ∏r2

The Attempt at a Solution


dA/dt = 2∏r(dr/dt)
dA/dt = 2∏r(3ft/s)

What now?
 
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Wa1337 said:

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. Does the area also increase at a constant rate?


Homework Equations


A = ∏r2

The Attempt at a Solution


dA/dt = 2∏r(dr/dt)
dA/dt = 2∏r(3ft/s)

What now?

Now you answer the question - Is the area increasing at a constant rate?
 
I mean, I guess it would, but I don't really know how to explain it.
 
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\pir (ft2/sec). Does that look like a constant to you?
 
Yes.
 
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.
 
Ok thanks I was very confused on this but you helped.
 
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