Originally Posted by

**scottshannon** I have a related rate question. I am an amateur mathematician...and I emphasize "amateur" here...and I have a question. I solved a related rate problem regarding the filling of a hemispherical tank. It is, I think, a standard problem in most calc 1 texts. Then I begin to wonder about how a full spherical tank fills. The first half of the filling of a spherical tank is the filling of the lower half and the second half is the filling of the upper hemisphere. I don't believe that the same method for calculating the rate of increase of the height per time is the same for filling the upper half is the same as for the lower half.

Then I began to think what happens if you just split the tank in two spherical halves and then put the upper half on the ground flat side down and began to fill it, assuming the flat side is down. I don't believe the same approach would work to finding dh/dt..would it? Or is dh/dt constant because the bottom is flat? I know that unlike when the bottom side fills, the height isn't always equal to the radius.

thanks...