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A spherical raindrop evaporates at a rate proportional to its surface area with (positive) constant of proportionality k ; i.E. The rate of change of the volume exactly equals ?k times the surface area. Write differential equations for each of the quantities below as a function of time.

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LammettHash

A sphere of radius [tex]r[/tex] has volume [tex]\dfrac43\pi r^3[/tex] and surface area [tex]4\pi r^2[/tex]. So

[tex]\dfrac{\mathrm dV}{\mathrm dt}=4\pi r^2k[/tex]

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