In tetrahedron A B C D, edge A B has length 3 \mathrm{~cm}. The area of face A B C is 15 \mathrm{~cm}^{2} and the area of face A B D is 12 \mathrm{~cm}^{2}. These two faces meet each other at a 30^{\circ} angle. Find the volume of the tetrahedron in \mathrm{cm}^{3}.