If you have a 3d shape how do you simplify the problem using symmetry. eg with a sphere is symmetric along any axis therefore the centroid must be in the middle of it eg2 A cone sitting on the xy plane, where the pointy bit is points up the z axis. -nb it is sitting on point (0,0,0) where the circular crossection lines on the xy plane at z = 0 with a centre at (0,0) you can intuitively see that the centroid must have an x coordinate of 0 and a y coordinate of 0 and there some random number for the z coordinate. where my understanding of symmetry is if a shape can be rotated about an axis and look the same then it is symmetric... this many not the be official definition though it seems to me that if a shape is symmetric across an axis, only a distance along that axis will need to be calculated to get the centroid. Is this right?