# Related rates of change are killing me!

by KingNothing
Tags: killing, rates
 P: 949 Hi. I am getting absolutely embarassed by these related rates problems. Here is one that I simply keep getting wrong: The volume of an expanding sphere is increasing at a rate of 12 cubed cm per second. When the volume is $$36\pi$$, how fast is the surface area increasing? $$V=\frac {4*pi*r^3}{3}$$$$S=4*pi*r^2$$ (how the heck do you use pi in latex? I know it's \pi, but that doesn't work right when Iput it in!) $$\frac {dV}{dt}=4 \cdot \pi \cdot r^2 \cdot \frac {dr}{dt}$$ Since volume is $$36 \cdot \pi$$, $$r=3$$. Correct?
 Mentor P: 40,711 Start by finding $dV/dt$ and $dS/dt$ in terms of r and $dr/dt$. (Hint: Chain rule)

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