(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The curve 3x^{2}+2y^{2}-12y=32 is rotated about the x-axis and forms a solid hemisphere.

Verify that the weight is 8cm from the bottom of the hemisphere.

2. Relevant equations

3. The attempt at a solution

Now, I can only do a little bit in centroids but that is for just plane surfaces. I do not think I know how to do it when it is rotated.

I thought it would be similar to the formula for centroids like

[tex]\overline{x}=\frac{\int x dA}{\int dA}[/tex]

would be similar to

[tex]\overline{x}=\frac{\int x dV}{\int dV}[/tex]

when rotated. I need some help in doing it.

EDIT:

I considered a cylindrical element of radius x and width dy.

So that the volume of this small element is [itex]dV= \pi x^2 dy[/itex]

Then I should have to take the first moment of volume about the x-axis? (like the first moment of area)

But I am not sure how to take this moment of volume

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# Homework Help: Centroid of a solid of revolution

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