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Problem relating to centroid

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The asking problem:
For the semiannular area, determine the ratio of r1 to r2 for which the centroid of the area is located at
x=-1/2*r2 and y=0.
Note: This problem is a 2D problem and not a 3D. It was taken from the «Distributed forces: Centroids and Centers of Gravity» section of my static course. The files is in word97 format for PC and not for Mac.

So, my question is how can I find this ratio of r1 to r2? I have none idea about that!!

If you will check your answers:
The response is 0.520

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Solution Summary

The semiannual area is examined. The ratio for the centroid of the area is determined.

Solution Preview

First, we need to solve for the x-coordinate of the centroid using the general equation. Then we can equate this with the given x-coordinate of the centroid (-r2/2), and then solve for the ratio r1/r2. See attached for details.

We are given a value of the centroid of -r2/2. We are told to find the ratio of r1/r2 that gives this value of the centroid, so we need an equation for the centroid, that we can equate to the given value. The centroid is a position (x, y). The general equation for an individual coordinate of the centroid of an object is:

where d indicates the integral is over all space, () is the density of the object as a ...

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