Breaking up the semi-circle into infinitesimally small rings

[spencerw105]

I attempted to solve this problem by breaking up the semi-circle into infinitesimally small rings of mass dm and width dr a distance r away from the center [0<r<R]. I then wrote dm in terms of the area: dm=pi*r*dr. Then, I plugged into the formula di=integral(dm*r^2) and integrated from 0 to R giving me .25*pi*R^4. This is not what I would have gotten for a complete disk though I would have gotten .5*pi*R^4 using the same process. Can someone please help I don't even know if I started correctly.

 

[haruspex]

I plugged into the formula di=integral(dm*r^2) and integrated from 0 to R giving me .25*pi*R^4. This is not what I would have gotten for a complete disk though I would have gotten .5*pi*R^4 using the same process. Can someone please help I don't even know if I started correctly.

You have left out a constant factor for density. What happens when you include that and express it in terms of the mass and area of the object?