By definition, centroid of an object is its geometric center. Centroid can be calculated as the center of mass assuming that the density is constant. Find the centroid for each solid. (a) The tetrahedron in the first octant enclosed by the coordinate planes and the plane cty+z=1. (0, 0, 1) (0. 1. 0) (1.0, 0) (b) The solid bounded by the surface z = y' and the planes r = 0, r = 1, z = 1