Science:Math Exam Resources/Courses/MATH101/April 2015/Question 09 (b)/Statement

A sculpture, shaped like a pyramid 3 m high sitting on the ground, has been made by stacking smaller and smaller iron plates on top of one another. The iron plate at height $z$ m above ground level is a square whose side length is $(3-z)$ m. All of the iron plates started on the floor of a basement 2 m below ground level.

Write down an integral that represents the work, in Joules, it took to move all of the iron from its starting position to its present position. Do not evaluate the integral. (You can use $9.8m/s^{2}$ for the force of gravity and $8000kg/m^{3}$ for the density of iron.)