- #1

- 3

- 0

## Homework Statement

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. For each case the right hand side should be a function of the dependent variable and the constant k. For example, the answer to the first question should not depend on S or r.

## Homework Equations

I was able to find dV/dt, dr/dt using mathematical models but I can't figure out why my answer isn't right for dS(surface area)/dt.

## The Attempt at a Solution

My dV/dt is -k\left(36\pi \right)^{\left(\frac{1}{3}\right)}V^{\left(\frac{2}{3}\right)}

My dr/dt is -k.

Because the equation for the surface area is 4*pi*r^2, the derivative of this would be 8*pi*r dr/dt.

Thus, this can be rewritten as -8k*pi*r. However, because my right side cannot include any independent variables, I must write by r in terms of Volume, which is r = (3V/4pi)^(1/3). So I put down my answer using these but in turns out its wrong so I'm kinda lost.