QUESTION: enter image description here

My working: I had divided the body into 5 common shapes which are shown here: enter image description 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: enter image description here

  • $\begingroup$ I cannot understand your table. :( Do you know the center of gravity of a circle? $\endgroup$
    – Jem Eripol
    Sep 25, 2017 at 11:18
  • $\begingroup$ 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. $\endgroup$
    – Surdz
    Sep 25, 2017 at 11:27
  • $\begingroup$ I will try to give inputs. $\endgroup$
    – Jem Eripol
    Sep 25, 2017 at 11:29
  • $\begingroup$ I think the only challenge here is to determine the centroid of a half circle. Am I right? $\endgroup$
    – Jem Eripol
    Sep 25, 2017 at 11:32
  • $\begingroup$ click this link and see what i had try: www53.zippyshare.com/v/HRgoVoQL/file.html $\endgroup$
    – Surdz
    Sep 25, 2017 at 11:45

1 Answer 1


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:

  1. $0.75(4)(7)$
  2. $\frac{\pi(2^2)}{2}(0.75)$
  3. $-\pi(1.25^2)(0.75)$
  4. $1(4)(2)$
  5. $-\frac{\pi(1.25^2)}{2}(1)$

Note: Negative areas as holes that need to be subtracted from the system.

X-Centroids are:

  1. $2$
  2. $2$
  3. $2$
  4. $0.5$
  5. $0.5$

Y-Centroids are:

  1. $-0.75/2$
  2. $-0.75/2$
  3. $-0.75/2$
  4. $2/2=1$
  5. $2-\frac{4(1.25)}{3(\pi)}$

Z-centroids are:

  1. $7/2$
  2. $7+\frac{4(1.25)}{3(\pi)}$
  3. $7$
  4. $2$
  5. $2$

You can then apply Varignon's Theorem to get the centroid.

  • $\begingroup$ 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 $\endgroup$
    – Jem Eripol
    Sep 25, 2017 at 11:48
  • 1
    $\begingroup$ And please understand how the values are taken. :) $\endgroup$
    – Jem Eripol
    Sep 25, 2017 at 11:53

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