Integration Engineering Problem

  • #1

Homework Statement

A cylinder of length 5 and diameter 2 units is constructed such that the density of the material comprising it varies as the distance from the base. If K is a proportionality constant such that the density is given by K * distance from base, use an integral to show that the
mass of the cylinder is given by : M =25Kpi/2

Homework Equations

Area of Circle : A = pi* r^2

The Attempt at a Solution

Fairly stuck with this question. Im not even sure where to begin with this. Im certain it isnt a very difficult problem but Im just not sure where to begin with it. Its going to consist of a definite integral somewhere along the line.
I understand that questions don't get answered without some sort of an attempt but im stumped at where to begin with this.

Answers and Replies

  • #2
Science Advisor
Homework Helper
Try slicing up the cylinder in little pieces of width dz.
If you take such a slice, at height z to dz, you can assume that its density is constant for sufficiently small values of dz. What is the mass then?

When you add this up for all slices, that will give you the definite integral you are looking for.