SOLUTION: A circular ripple spreads across a lake. If the area of the ripple increases at a rate of 10pi m^2s^-1, find the rate at which the radius is increasing when the radius is 2 m.

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Question 1191911: A circular ripple spreads across a lake. If the area of the ripple increases
at a rate of 10pi m^2s^-1,
find the rate at which the radius is increasing when the radius is 2 m.
Found 2 solutions by Edwin McCravy, ikleyn:
Answer by Edwin McCravy(20059) About Me  (Show Source):
You can put this solution on YOUR website!
A circular ripple spreads across a lake. If the area of the ripple increases
at a rate of 10pi m^2s^-1,
That means dA%2Fdt=10pim%5E2%2Fs

We want a formula for the area of a circle.

A=pi%2Ar%5E2
dA%2Fdt=2%2Api%2Ar%2Aexpr%28dr%2Fdt%29
Substitute 10pi for dA%2Fdt and simplify

find the rate at which the radius is increasing when the radius is 2 m.
Substitute 2 for r
Solve for dr%2Fdt

Edwin

Answer by ikleyn(52798) About Me  (Show Source):
You can put this solution on YOUR website!
.

Physically, when a stone is dropped into a still pond sending out a circular ripple of the radius r = r(t),

the rate %28dr%29%2F%28dt%29 is constant and is equal to the speed of surface wave.

The area of the circle is a quadratic function of time, in this case.


So, in reality, the radius r= r(t) and the area A = A(t) are different types of functions, distinct of described in this problem.


You may find many Internet sources, related to this phenomenon.