A hemispherical bowl with radius 8-inches is filled with punch (weighing .04 pound/in^3) to within 2-inches of the top. How much work is done emptying the bowl if the contents are pumped just high enough to get over the rim?
The Attempt at a Solution
Work = Force(weight)* displacement.
i said displacement was "x"
and for the weight:
r = sqrt(64- x^2)
weight = (.04) (pi * r^2)dx
and so, work to lift weight at a given "x"
so i get total work is
integration from 2 to 8 of
(.04pi)(x)(64 - x^2)dx
Is this the right way to approach this problem?