# 2.21: Tetrahedra

Exercise \(\PageIndex{1}\)

Show that the moment of inertia about an axis through the centre of mass of a uniform solid regular tetrahedron of mass \(m\) and edge length \(a \) is \( \frac{1}{20} ma^2 \)

Exercise \(\PageIndex{2}\)

Show that the moment of inertia of a methane molecule about an axis through the carbon atom is \( \frac{8}{3} ml^2 \) , where \( l \) is the bond length and \( m \) is the mass of a hydrogen atom.

And, in case you are wondering that I haven’t specified the *orientation* of the axis in either case, the solid regular tetrahedron and the methane molecule are both spherical tops, and the moment of inertia is the same about* any* axis through the centre of mass.