



 
Ray, You called this problem a related rates problem and you are correct. The fundamental question as I see it is how to you relate what is going on inside the filter to what is going on inside the cylinder. The water is flowing from the filter into the cylinder so the volume of the water in the filter is decreasing at the same rate as the volume of the water in the cylinder is increasing. To say this mathematically I need some variables. Let t be the time measured in minutes, V_{f} be the volume of the filter measured in cubic centimeters and V_{c} be the volume of the cylinder measured in cubic centimeters. The fact I know then is
Suppose at some time t the height of the water in the filter is h_{f}, the radius of the surface of the water in the filter is r_{f} and the height of the water in the cylinder id h_{c}, all measured in centimeters. Thus you know that
and
Use similar triangles to express V_{f} in terms of h_{f} alone. Differentiate V_{f} and V_{c} with respect to t. Relate the expressions using equation (*). Substitute the values you know when h_{f} = 12 cm, nd solve for dh_{c}/dt. Harley  


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