Centroids Simplifying by symmetry

1. Sep 29, 2009

SpartanG345

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?

2. Sep 30, 2009

tiny-tim

Hi SpartanG345!
It's good enough!
("symmetric about an axis")

Yup, that's completely right!