Hi, i need some help on this.

a) Determine the volume dV of the cylindric(?) shell in the figure.

the curve is y=16-x^2

I took a picture of the image in the book, might help

http://img452.imageshack.us/my.php?i...ture022oj5.jpg

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- Nov 17th 2006, 11:54 AMJonesRotating circle
Hi, i need some help on this.

a) Determine the volume dV of the cylindric(?) shell in the figure.

the curve is y=16-x^2

I took a picture of the image in the book, might help

http://img452.imageshack.us/my.php?i...ture022oj5.jpg - Nov 17th 2006, 12:29 PMCaptainBlack
- Nov 17th 2006, 12:37 PMJones
- Nov 17th 2006, 12:41 PMCaptainBlack
The circumference of the shell is $\displaystyle 2 \pi\ x$ the thickness is

$\displaystyle dx$ the height is $\displaystyle y$. To first order in $\displaystyle dx$ the volume is:

$\displaystyle

dV= (2 \pi x) y dx

$

If you want it more explicit its the difference in volume of the two cylinders of radius $\displaystyle x$

and $\displaystyle x+dx$ of heights $\displaystyle y(x)$ and $\displaystyle y(x+dx)$ or:

$\displaystyle

dV= -\pi x^2 y(x) + \pi (x+dx)^2 y(x+dx)=\pi\ 2 \ x\ dx (16-x^2) +O(dx^2)

$

RonL