Calculate Work Homework: Hemispherical Tank Full of Water

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To calculate the work required to pump water from a hemispherical tank, the integral setup involves the equation pi*(5-h)(25-h^2)dh, evaluated from 0 to 5. The initial attempt at solving the integral resulted in an expression that did not yield the correct answer. The error identified was the omission of the water's density, which is crucial for accurate calculations. Incorporating the density of water, 62.5 lb/ft3, into the integral is necessary for determining the total work required. Properly adjusting the integral with this density will lead to the correct solution.
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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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