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Calculus/Differential Equations

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Expert: - 1/24/2010


Question
Hello
I am having problems with writing the differential equation to:

"A spherical raindrop evaporates at a rate proportional to its surface area. Write a differential equation for the volume of the raindrop as a function of time."


Answer
The volume V = 4πr³/3 and the surface area is 4πr².

The rate of change of volume is dV/dt, where r is a function of t.
This meand dV/dt = 4πr²r'(t), and r'(t) is said to be some constant, say k.

So, dV/dt = 4πr²k, and A = 4πr², so dV/dt = kA.

Is that the differential equation you're looking for?

Calculus

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