and the plane
if S has constant density K.
Solution: When a = 1 the solid S has the shape of a sausage:
As for its center of mass:
Going on to the centroid:
Center of mass:
Since the region is symmetric with respect to the x and y axis
.
Going on to the y-coordinate:
Since the mass is
,
the center of mass is
,
which is plausible, for most of the mass of the sausage is in its upper part.
by:sh