how to calculate center of mass of symmetrical bodies like sphere,rectangle which you asked in video?

symmetrical bodies having homogenous distribution of mass over the volume:

 

we take a elemental volume at a particular distance

then we integrate it over the whole object to calculate the mass

center of mass is defined as:

R = ?(M.r)/?r

thus here it will be R = ?M.r dr/?dr               (here M is a function of r)