1 Attachment(s)

Z-coordinate of centroid , centre of mass prob

Hi!

**Problem:** Determine the z-coordinate of the centroid of the solid generated by revolving the quarter-circular area thorugh 90 degress about the z-axis.

**Solution attempt:**

I tried to calculate the volume of the solid. I got it to be $\displaystyle \frac{\pi a^{3}}{24}(4+3\pi)$

I have some trouble setting up the sum of moments integral, that is $\displaystyle \int z_{c} \; dz = V\bar{z} $

I tried to use a horizontal strip as differential element:

Witdh: $\displaystyle \sqrt{a^{2}-z^{2}}$

Height: $\displaystyle dz$

Moment arm: $\displaystyle z$

But I also need thickness, right? expressed in terms of z

Thx!