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M3 centre of mass of hemisphere

A closed container C consists of a thin uniform hollow hemispherical bowl of radius a, together with a lid. The lid is a thin uniform circular disc, also of radius a. The centre O of the disc coincides with the centre of the hemispherical bowl. The bowl and its lid are made of the same material.

Show that the centre of mass of C is at a distance (1/3)a from O

I know that the CoM of the bowl bit is 1/2a from O and obviously the CoM of the lid is at O but cannot work it out for the entire body. Do i need to take moments?...if so how do i know the weight of a hemispherical shell?