$\"\"$

The equations are $\"\"$ and $\"\"$ .

The surface area of the sphere is $\"\"$ .

The arc length of $\"\"$ is $\"\"$ .

The distance traveled by the centroid is $\"\"$ .

Substitute $\"\"$ and $\"\"$ .

$\"\"$

$\"\"$ .

The circumference of the circle of radius $\"\"$ is $\"\"$ .

The distance traveled by the centroid is equal to the circumference of the circle.

$\"\"$

$\"\"$ .

Therefore, the centroid of the semicircle $\"\"$ is $\"\"$ .

$\"\"$

$\"\"$ .