statics

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Let A be a point on the X axis. The total area of the figure left of A is equal to the total area of the figure right of A. Find A's X coordinate.

>>340665
You puled some of those numbers out of thin air. Technically.

>>340676
It doesn't matter, the principle stays the same, assuming the shape is of uniform density.

>>340665
That doesn't work because a unit square 10 from the axis represents a ring with a volume ~10 times that of a unit square on the axis.

Your technique would work if that were an extruded prism, but it's not so it doesn't.

You need to convert the shape into a function, integrate it, then find the middle of the sum over it.

>>340657
>>340665
>http://tutorial.math.lamar.edu/Classes/CalcII/CenterOfMass.aspx

>>340830
or use formulas and never learn how things work
>https://en.wikipedia.org/wiki/List_of_centroids

>>340657
http://www.mathcentre.ac.uk/resources/uploaded/mc-ty-volumes-2009-1.pdf

Find the formula for the hemisphere, the cone, and the cylinder, compose them into a function, and integrate it. The figure has rotational symmetry and uniform density, so you know the center of mass is on the X axis, and all you're really trying to find is how far along the X axis you have to go until half the volume is behind you. You can find this by integrating to find the formula for the volume from zero to x.

OP, ignore the following posts:
>>340665
>>340679
>>340830
>>340832
They're talking about finding the center of mass of a 2D cross-section of this THREE DIMENSIONAL SHAPE, which is not what the question is asking for, and is not a calculus question but a pre-calculus question.

>>340890
>They're talking about finding the center of mass of a 2D cross-section of this THREE DIMENSIONAL SHAPE, which is not what the question is asking for
> The figure has rotational symmetry and uniform density, so you know the center of mass is on the X axis, and all you're really trying to find is how far along the X axis you have to go until half the volume is behind you.

>pre-calculus question
>You can find this by integrating to find the formula for the volume from zero to x.

contradicting with yourself this much
seriously?!

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I appreciate all of you for the help. 340890 give me a good clue about ir and finally i found it

>>340897
The thing you made up then answered was the precalculus question, ESL-kun.