Calculate Work Homework: Hemispherical Tank Full of Water

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SUMMARY

The discussion focuses on calculating the work required to pump water out of a hemispherical tank, where water weighs 62.5 lb/ft³. The initial integral setup was incorrect, as it did not account for the density of water. The correct integral to compute the work is the integral from 0 to 5 of the function pi*(5-h)(25-h²)dh, leading to the correct work calculation of (3125/12)*pi ft-lb after proper evaluation.

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Homework Statement



The hemispherical tank shown is full of water. Given that water weighs 62.5 lb/ft3, find the work required to pump the water out of the tank. (the water will be pumped out of a spigot at the top)

Homework Equations



INTEGRAL from 0 to 5 of: pi*(5-h)(25-h^2)dh

The Attempt at a Solution



INTEGRAL from 0 to 5 of: pi*(h^3-5h^2-25h+125)dh

pi*((h^4)/4 - (5h^3)/3 - 12.5h^2 + 125h)

= (3125/12)*pi ft-lb.

This answer is incorrect though...anyone know what I am doing wrong? Thanks.
 
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You didn't use the density of water data. How would you incorporate this?
 

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