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## 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?