A box, open at the top, in form of a cube of edge length 40 cm, is constructed from a metal plate. Find the coordinates of the center of mass of the box with respect to x, y, and z coordinate system.

Answer 1

Let the box bottom be centered at the origin, with sides parallel to the x and y axes.

The center of mass is at x = 0 and y = 0 for reasons of symmetry. For the z coordinate, take the area-weighted mean of the z coordinates of the centers of the four sides and bottom. That would be
z = 4*20/5 = 16 cm

(0,0,16)