Science:Math Exam Resources/Courses/MATH101/April 2012/Question 06/Statement

A tank in the shape of a hemispherical bowl of radius 3m, with an outlet that rises 2m above its top (see the diagram below), is full of water. Using the fact that the density of water is $1000{\text{kg/m}}^{3}$, find the work (in joules) required to pump all the water out of the outlet. You may use the value $g=9.8{\text{m/s}}^{2}$ for the acceleration due to gravity. You do not need to simplify your answer, but you must completely evaluate any integral(s) that arise.

Diagram for the above question