Final answer:
The centroid of a semicircle with a radius of 9 units, centered at the origin, and whose diameter lies along the y-axis, is approximately located at (0, 3.8197).
Step-by-step explanation:
The question pertains to finding the centroids of certain geometric shapes. Specifically, it asks to find the centroid of a semicircle whose diameter lies along the y-axis, with its center at the origin of the coordinate system.
To find the centroid of such a semicircle, one must use the formula for the centroid of a semicircle of radius R, which is located at a distance of 4R/(3π) above the center along the y-axis. Since the semicircle passes through the point (9,0), it has a radius of 9. The coordinates of the centroid would therefore be (0, 4*9/(3π)) or approximately (0, 3.8197).