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 [tex]36\pi[/tex], how fast is the surface area increasing? [tex]V=\frac {4*pi*r^3}{3}[/tex][tex]S=4*pi*r^2[/tex] (how the heck do you use pi in latex? I know it's \pi, but that doesn't work right when Iput it in!) [tex]\frac {dV}{dt}=4 \cdot \pi \cdot r^2 \cdot \frac {dr}{dt}[/tex] Since volume is [tex]36 \cdot \pi[/tex], [tex]r=3[/tex]. Correct?
Start by finding [itex]dV/dt[/itex] and [itex]dS/dt[/itex] in terms of r and [itex]dr/dt[/itex]. (Hint: Chain rule)