(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the work required to empty a 10m high conical tank with a radius at the top of 4m by pumping the water out the top of the tank. The water level is 2m below the top of the tank.

2. Relevant equations

[itex]\pi r^2[/itex]

Similar triangles

3. The attempt at a solution

General formula for the radius:

[itex]\frac{4}{10} = \frac{r}{(10-x)}[/itex] where x = distance from the top of the tank.

[itex]r = \frac{2}{5}(10-x)[/itex]

Therefore, the volume of any given slice [itex]= \pi(\frac{2}{5}(10-x))^2\Delta x[/itex]

This is where I get a bit confused. What do I need to multiply my volume formula by when I integrate from x = 2 to x = 10?

Also, after I have multiplied my volume by the whatever I need to (distance?) and integrated between 2 and 10, have I pumped the water out the top of the barrel or only to the top of the water level? Do I need to add +2m to something somewhere?

Thanks.

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# Work required to pump water out of a conical tank

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