W = weight density of the fluid

A = cross-sectional area as a function of y

L = lift distance of a representative horizontal cross section as a function of y

T = cross sectional thickness ... dy

sketch the graph of the circle ... use the lower half to represent the edge of the bowl.

radius of a representative horizontal "slice" of liquid is r = x, so cross-sectional area ...

lift distance of a representative 'slice" ...

weight density of water is

all the "slices" of water lie between and

work in Joules is given by ...