Such as a figure formed by a semicircle rotating once around the diameter, the center of gravity of the semicircle

abscissa

for

4r

/3π

The distance that the center of gravity moves is 2π(4r/3π).

The area of a semicircle is 1/2πr?

Then the volume is: 2π(4r/3π)* 1/2πr? =4/3πr？