(Solved):   A reservoir has the shape of a truncated cone as shown in the figure above. It measures \( ...

 

A reservoir has the shape of a truncated cone as shown in the figure above. It measures \( 4 \mathrm{~m} \) high. The radius of the base is \( 3 \mathrm{~m} \) and the top radius is \( 4 \mathrm{~m} \). It is filled with water. We want to calculate the amount of work required to pump all of its water through the hose standing \( 2 \mathrm{~m} \) above the reservoir. (i) Let \( x \) be the height in metres measured from the base of the reservoir. The weight of a thin water layer between heights \( x \) and \( x+\Delta x \) is approximately \( P(x) \Delta x \). What is \( P(x) \) ? \( P(x)= \) Q \( \Sigma \) FORMATTING: Express the answer as a function of \( x \).