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?

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Science is not about memorizing formulas and numbers.

Well center of mass can be easily calculate if the body is symmetrical and of uniform density. Here in all of these problems you can argue that about which point the mass distribution is same.
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No, its not necessary that center of mass of any body having uniform density lie inside the body. For sphere, Cylinder and cube the centre of mass lie in side body but for a ring Center of mass lie out side of the body where is no mass.
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