Question 601881
"its volume increases at a rate proportional to its radius"


Therefore, *[tex \LARGE \frac{dV}{dt} = Cr] where C is a constant. However we also know that


*[tex \LARGE V = \frac{4}{3}\pi r^3 \Rightarrow \frac{dV}{dt} = 4\pi r^2 \frac{dr}{dt}]


because the souffle is shaped like a sphere. Substitute into the first equation to obtain


*[tex \LARGE 4\pi r^2 \frac{dr}{dt} = Cr]


Solve for dr/dt


*[tex \LARGE \frac{dr}{dt} = \frac{C}{4\pi r} = \frac{k}{r}] (k is another constant).