# Shell method versus disk method

1. May 6, 2008

### fiziksfun

I'm confused when to use the shell method vs. the disk method

Specifically in this problem:

If the region encolsed by the y-axis, the line y=2 and the curve y=$$\sqrt{x}$$ is revolved around the y-axis, the volume of the solid generated is:

However when I use the shell method and the disk method I get different answers

Can someone tell me what I'm doing wrong?

Disk Method:
$$\pi$$ $$\int$$y^4 dy evaluated from 0 to 2

Shell Method:

2$$\pi$$$$\int$$x(2-$$\sqrt{x}$$)dx