Subject: calculus related rates

Name: molly

Who is asking: Student
Level: Secondary

A tanker spilled 30 ft cubed of chemicals into a river, causing a circular slick whose area is expanding while its thickness is decreasing. If the radius of the slick expands at the rate of 1 foot per hour, how fast is them thickness of the slick decreasing when the area is 100 feet squared?


i figured out a bunch of stuff but i don't know what to do:

Area=(pi)r 2 A=100ft 2 so... r= 5.64ft
Volume=(Area)(height) V=30ft 3 so... h=0.3ft when area is 100ft 2 dr/dt=1ft/hr dA/dt=(pi)2r(dr/dt)
V=(A)x(h) so... h=V/A so... dh/dt= (dV/dt)/(dA/dt)

Hi Molly,

You're on the right track most of the way but look at your last line: you have h = V/A and then an expression for dh/dt; you're not doing this step correctly and further you are not using the fact that V is constant.

If f(x) = c/x where c is a constant, what would  d/dx(f(x)) = f'(x) be?

-c/x 2.

Now what happens if you want  d/dt(f(x))?


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