Hi!

Problem:Find x-coordinate of centroid of the solid spherical segment.

Solution attempt:

$\displaystyle dV=\pi\cdot r^{2} \cdot dx $

I need to express $\displaystyle r$ in terms of $\displaystyle R \mbox{ and } x $ .

I did, (and this part is probably wrong): $\displaystyle \frac{R}{R}=\frac{r}{\frac{R}{2}-x} \, \Rightarrow \, r = \frac{R}{2}-x $

And for the moment arm I used $\displaystyle \frac{R}{2}+x$

Then integrate from $\displaystyle \frac{R}{2} \mbox{ to } R $

I have solved it now, and OMG did my first solution attempt suck, dont read it