Need: a math wizard! (Calculus related rates)

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Hello,

I'm taking an AP Calculus class online as an honors course and have been doing pretty well with the first few chapters of the course. However, I've really hit a road block with related rates problems. The trouble I'm having is that I follow all the directions given in the tutorials and I still come up with a hugely complicated equation and usually the wrong answer.

It says to draw a picture, but that doesn't help much when I don't understand what the problem is asking for in the first place.

It's a problem like this that I'm referring to:

[spoiler]A circular oil slick of uniform thickness is caused by a spill of 1 cubic meter of oil. The thickness of the oil is decreasing at the rate of 0.3 cm/hr as the slick spreads. At what rate is the radius of the slick increasing when it is 17 meters?[/spoiler]

Any tips on visualizing this would be appreciated.

Thank you,

~Saiyan

Scenario looks like this for your example:



I can't think of how to explain how to get there asides from practise and having done enough of these questions during my year 11 + 12:
-draw a picture (ie if it says a cone somewhere in the question, draw a cone.)
-write what you need to find (ie dr/dt in your example)
-write down what you already know (ie d(thickness)/dt = 0.3)
-write down something using the chain rule that connects the two (dr/dt = d(thickness)/dt * dr/d(thickness))
-the question should have given you enough information to find our new rate dr/d(thickness) using your picture (ie we know 1m^3 = pi r^2 t, so can rearrange this, then differentiate it)
-shove appropriate numbers in to get answer

A thing that always helps me with this problem is that the rate (xxx meters per second, centiliters lost per minute, etc.) is always the derivative of a function with respect to time.

it will be a cylinder with a small thickness. The thickness is decreasing and the radius is increasing as the "puddle" spreads.

the volume is 1m^3. this will not change so you can set the equation for the cylinder to equal 1.

as the thickness decreases the radius will have to increase at a related rate to accommodate the same volume of oil.

They give you the rate of the thickness decrease and the radius at which you must find the instantaneous rate of change.

the volume equals 1. the equation for the volume of a cylinder is



the derivative is a function of the change in h (which you know) and the radius. plug in the radius of 17. and figure out the rate.

Thank you all. =)

Haha, related rates sure do suck.