((I cannot, for the love of life, understand related rates, so please bear with me. Thank you! ))
A cylindrical tank with radius 5m is being filled with water at a rate of 3m3/min. How fast is the height of the water increasing?
I'm having trouble interpreting this question - actually, most related rates questions, having trouble differentiating between what I would call the volume and what not.
The Attempt at a Solution
So, I'm going to say that I know the rate of change of the volume - which means I need to get the height in terms of the volume?
since v= (pi)r2h
h' = (dy/dx [v]((pi)r2) - dy/dx[(pi)r2](v))/((pi)2r4)
h' = (3(2pir^2) - 2pirv)/ ((pi)2r4)
I'm pretty sure this is wrong since I ended up with a "v" in my numerator which I don't know the value of.
How would I go about solving this?