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Related rate problem

Name: Anonymous 2006-10-28 14:29

This problem has been giving me trouble for a couple of hours now.  How would you find the initial volume of a sphere, given only the rate at which the circumference is decreasing and the time that it takes for the volume to reach 0?

I figure I should start with C=2pi(r) and use implicit differentiation to get dC/dt = 2pi(dr/dt), but where do I go after I solve for dr/dt?

Name: Anonymous 2006-10-28 14:49

V = 4/3*pi*(r^2)

once you have dr/dt you can find dV/dt and write a formula for V(t)

Name: Anonymous 2006-10-28 14:49

V = 4/3*pi*(r^3) sorry lolz 3 dimensions

Name: Anonymous 2006-10-28 14:58

Already tried that, I ended up with dV/dt=(4(dr/dt))r^2. 4(dr/dt) is a constant. In short, I need to know what to do with
dV/dt = (constant)r^2.

Name: Anonymous 2006-10-28 16:27

youve got a formula for dr/dt, if you know an initial r, you know r after t seconds.  V is in terms of r.  write r in terms of t.

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