Emptying a Bowl: Calculating Work

[teken894]

Homework Statement

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?

Homework Equations

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"
is weight*displacement

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?

 

[Werg22]

Is it being pumped from underneath so that there is free space between the liquid and the bowl?

 

[HallsofIvy]

Yes, that is exactly right!