It occured to me that most unification theories propose at least 6 dimensions, and that the 6th dimension would look like a sphere or a doughnut. For the sake of greater simplicity, I will use a sphere for my question. My question is, if an object were travelling in the 6th dimension, would they be travelling 'in' or 'on' the the 6D sphere? Also, is the 6D sphere a 2D sphere embedded in 3D space plus time, or is it a 6D sphere, as in 5D + Time? For instance, if you wanted to find the surface area of the sphere, would you use the regular equations of a 2D sphere, because it is a sphere embedded in 4D space-time, or would you use the equation for surface area of a 5D sphere and add time? Thanks in advance.