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Related rates of change are killing me!

by KingNothing
Tags: killing, rates
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Mar16-06, 03:25 PM
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 [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?
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Doc Al
Mar16-06, 03:30 PM
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P: 41,477
Start by finding [itex]dV/dt[/itex] and [itex]dS/dt[/itex] in terms of r and [itex]dr/dt[/itex]. (Hint: Chain rule)

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