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December 18, 2014

December 18, 2014

Posted by **joelle** on Thursday, April 8, 2010 at 11:32am.

a. How fast is the area of the slick expanding?

b. If the circular slick has the same thickness as everywhere, and the volume of oil spilled remains fixed, how fast is the thickness of the slick decreasing?

- math please help -
**Reiny**, Thursday, April 8, 2010 at 11:48amArea = πr^2

dA/dt = 2πr(dr/dt)

for the given data

dA/dt = 2π(150)(.1) m^2/min

= 94.25 m^2/min

Volume = Areax height = Ah

dV/dt = A(dh/dt) + h(dA/dt)

so when r = 150, A = π(150)^2 = 22500π

dV/dt = 0 (it remains constant) and

h = .02

0 = 22500π(dh/dt) + .02(94.25)

dh/dt = - .02(94.25)/22500π

= - .000026667 m/min

check my arithmetic

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