$\"\"$

\

Observe the figure :

\

The engine is approximately $\"\"$ above the top of the fuel tank.

\

Weight of the diesel fuel is approximately $\"\"$ .

\

Since the engine is approximately $\"\"$ above the top of the fuel tank the volume can be considered as Volume, $\"\"$ .

\

The force is calculated by $\"\"$ .

\

The force of pushing one rectangle with depth $\"\"$ is $\"\"$ .

\

$\"\"$ .

\

$\"\"$

\

The work done can be calculated by using the formula $\"\"$ .

\

Since the height of the engine is $\"\"$ above the top of the fuel tank the limit ranges from $\"\"$ to $\"\"$ .

\

$\"\"$ .

\

$\"\"$ , so write in the terms of $\"\"$ .

\

$\"\"$

\

$\"\"$

\

Apply integration :

\

$\"\"$

\

$\"\"$

\

The work done by the fuel pump in raising the fuel tank of fuel to the level of the engine is $\"\"$ .