A tank has the shape of a truncated cone as in the figure above. He does $m$ high. Its radius at the base is $m$ of and the one at the top is of $m.$ It is filled with

water. We want to calculate the work required to pump all its water through the pipe to $m$ above the tank.

$($i$)$ Either the height in meters measured from the bottom of the tank. The weight of a thin layer of water between the heights and is about

$.$ What is $?$

$$

Express the answer with a formula. It is recalled that the density of water is

surface is

$($ii$)$ The work in Joules required to pump this thin layer of water to $m$ above the tank is about

$$

Express the answer with a formula.

and that the gravitational acceleration on the earth's

$.$ What is

$?$