Can anyone help me with 29.I know how to find centroids when one function is given but in this one I don't think that knowing only the function of circle or rectangle will help us.I found that there is something called additive centroids but I don't know how that one works here.Can anyone fully explain this task and additive centroids please?
As you can probably guess (by symmetry or intuition), the centroid of the rectangle is at $C_1 =(0,h/2)$. Now the centroid of semicircle is actually $\frac{4r}{3\pi}$ above the centre of the circle which in our case makes it
$$C_2 = (0,h+\frac{4a}{3\pi})$$
To calculate the centroid of the entire figure you simply use weighted averages
$$C = \frac{C_1\cdot 2ah + C_2\cdot\pi r^2}{2ah+\pi r^2}$$
You can take it from here, I believe.
Reference - http://datagenetics.com/blog/january52017/index.html