QUESTION: 
My working: I had divided the body into 5 common shapes which are shown here:
now that I'm solving for x bar, y bar, and z bar I find it difficult in finding the x, y and z directions.
see my table of working here: 
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5
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$\begingroup$ I cannot understand your table. :( Do you know the center of gravity of a circle? $\endgroup$– Jem EripolCommented Sep 25, 2017 at 11:18
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$\begingroup$ first column is the volume calculation of the shape, the second column is the x bar or x direction of the shape, same as y and third is the x direction multiply by volume and sames as for y. the element had been divided into five common shapes, two rectangular, two half cylinders and one cylinder. $\endgroup$– SurdzCommented Sep 25, 2017 at 11:27
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$\begingroup$ I will try to give inputs. $\endgroup$– Jem EripolCommented Sep 25, 2017 at 11:29
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$\begingroup$ I think the only challenge here is to determine the centroid of a half circle. Am I right? $\endgroup$– Jem EripolCommented Sep 25, 2017 at 11:32
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$\begingroup$ click this link and see what i had try: www53.zippyshare.com/v/HRgoVoQL/file.html $\endgroup$– SurdzCommented Sep 25, 2017 at 11:45
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1 Answer
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Try this one. (Note: I don't know how to do tables in this site but please tabulate the data on your own.)
Areas are:
- $0.75(4)(7)$
- $\frac{\pi(2^2)}{2}(0.75)$
- $-\pi(1.25^2)(0.75)$
- $1(4)(2)$
- $-\frac{\pi(1.25^2)}{2}(1)$
Note: Negative areas as holes that need to be subtracted from the system.
X-Centroids are:
- $2$
- $2$
- $2$
- $0.5$
- $0.5$
Y-Centroids are:
- $-0.75/2$
- $-0.75/2$
- $-0.75/2$
- $2/2=1$
- $2-\frac{4(1.25)}{3(\pi)}$
Z-centroids are:
- $7/2$
- $7+\frac{4(1.25)}{3(\pi)}$
- $7$
- $2$
- $2$
You can then apply Varignon's Theorem to get the centroid.
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$\begingroup$ I just edited. I made a mistake looking at the location of the x-axis. Y-centroids for areas 1,2, and 3 should be negative $\endgroup$ Commented Sep 25, 2017 at 11:48
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1$\begingroup$ And please understand how the values are taken. :) $\endgroup$ Commented Sep 25, 2017 at 11:53