Observe the graph :

The first function above the -axis represents half of the semicircle.

Semicircle with radius units is in the form of

The first function is .

The second function below the -axis represents a line equation.

line equation passing through the points is  and is

The second function is .

The value of density is .

From the graph the limits are .

The formula for is .

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Substitute the values and density , which is in the formula.

Substitute .

The formula for is .

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Substitute the values and density which is in the formula.

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The center of mass is equal to the centroid of the shape.

To Find the coordinates of the centroid divide respectively by the area and density .

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First find the area :

Apply the integration method to find the area of the curve.

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Therefore the area is .

Therefore the center of mass can be calculated by using the formula : .

Therefore .