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Homework Statement
The curve 3x2+2y2-12y=32 is rotated about the x-axis and forms a solid hemisphere.
Verify that the weight is 8cm from the bottom of the hemisphere.
Homework Equations
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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