Center of gravity of this body: y = (x^2)/a (rotated about the x-axis)

[Heexit]

Homework Statement

A homogeneous body is formed by rotating the surfaces in the image around the x-axis (see picture). Determine the location of the center of gravity.

Relevant Equations

N/A

Hello Physicsforum!

My solution (sorry for not writing it in LaTeX, I don't feel it's necessary since this try was more of a shot in the dark):

The answear should be (5/6)*a

Had no idea of how to go about solving this, so tried using the followin equaiton (I have no idea what W stands for in this case, but it can be switched out for mass/volume/area):

Any suggestions about what could have gone wrong alternatively what I should do instead would be appreciated!

Thanks on beforehand

 

[Lnewqban]

W could means weight.

 

[kuruman]

This is a solid of revolution. It looks like you need to use $$\bar X=\frac{\int x~ dV}{\int dV}$$where $dV$ is the volume of a disk of thickness $dx$ and radius $y$.

 

[Heexit]

This is a solid of revolution. It looks like you need to use $$\bar X=\frac{\int x~ dV}{\int dV}$$where $dV$ is the volume of a disk of thickness $dx$ and radius $y$.

Thanks a lot for your help!
Here is my solution (still not in LaTeX!):

 

[kuruman]

Looks OK even though not in LaTeX. Your letter ex in places looks a bit like the Greek letter alpha and that could be confusing.