The problem involves a circular ripple created by a stone dropped into a pond, with the radius increasing at a constant rate of 3 ft/s. The central question is whether the area of the circle also increases at a constant rate.
Some participants have provided insights into the mathematical relationships involved, noting that the rate of change of area is dependent on the radius. There is an acknowledgment of confusion regarding the constancy of the area change rate, with some clarification offered.
Participants express uncertainty about the implications of the variable nature of the area change rate as it relates to the radius. The discussion reflects an exploration of assumptions about constant rates in the context of changing dimensions.
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?