# Work required to pump water out of a conical tank

## Homework Statement

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.

## Homework Equations

$\pi r^2$

Similar triangles

## The Attempt at a Solution

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

$r = \frac{2}{5}(10-x)$

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

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.