Give the location of the centre of mass of a $(i)$ sphere,$(ii)$ cylinder,$(iii)$ ring,and $(iv)$ cube,each of uniform mass density. Does the centre of mass of a body necessarily lie inside the body?

(N/A) The centre of mass $(C.M.)$ of a body with uniform mass density is located at its geometric centre.
$(i)$ For a sphere,the $C.M.$ is at its geometric centre.
$(ii)$ For a cylinder,the $C.M.$ is at its geometric centre (midpoint of the axis).
$(iii)$ For a ring,the $C.M.$ is at its geometric centre.
$(iv)$ For a cube,the $C.M.$ is at its geometric centre.
No,the centre of mass of a body does not necessarily lie inside the body. For example,in the case of a ring or a hollow sphere,the $C.M.$ lies at the geometric centre,which is in the empty space outside the material of the body.