The centroid of a rectangular solid in the first octant with vertices (0, 0, 0), (0, 0, 4), and (4, 4, 4) is
B) (0, 2, 4)
C) (2, 2, 2)

Question

The centroid of a rectangular solid in the first octant with vertices (0, 0, 0), (0, 0, 4), and (4, 4, 4) is
B) (0, 2, 4) 
C) (2, 2, 2)

Quizplus · Accepted Answer

The centroid of a solid is given by the average of the coordinates of all its vertices. In this case, the three vertices have coordinates (0, 0, 0), (0, 0, 4), and (4, 4, 4). The average of the three x-coordinates is (0+0+4)/3=4/3, the average of the three y-coordinates is (0+0+4)/3=4/3, and the average of the three z-coordinates is (0+4+4)/3=8/3. Therefore, the centroid is (4/3, 4/3, 8/3), which is closest to choice C.

The Centroid of a Rectangular Solid in the First Octant