- #1

squelch

Gold Member

- 57

- 1

I just want some sanity checking on my procedure, since I'm not this far in my calculus course yet but am having to work through it anyway for physics.

I have no idea how to approach part c, not even an inkling of where to begin. If all you give me are Google search terms, then I'll be happy.

## Homework Statement

A cylinder of radius R and length L is given.

a) Use the shell method to write the infinitesimal volume DV

b) Integrate dv to obtain the volume of the cylinder.

c) The density of the cylinder is given by [itex]\rho = {\rho _0}(1 - \frac{r}{R})[/itex] where [itex]{\rho _0}[/itex] is constant.

## Homework Equations

NA.

## The Attempt at a Solution

a) A cylinder can be divided into infinitesimal shells of height L and width dr. Therefore, the infinitesimal volume is given by:

[tex]dv = 2\pi LRdr[/tex]

b) This infinitesimal volume can then be integrated as:

[tex]V = \int_0^R {2\pi LRdr = 2\pi LR\int_0^R {dr = 2\pi LR(\left. r \right|_0^R) = 2\pi L{R^2}} } [/tex]

c) No idea.