Why can you cook using microwaves, but not with radio waves or infra red etc?

Answer 1

You can, but the frequency chosen (3.5 GHz or so) corresponds to a resonance of the H20 molecule, so it absorbs the energy more readily. BTW infrared *is* commonly used for cooking. It's called broiling or toasting, depending on the food. It only heats the surface directly since IR doesn't penetrate food very far.

Answer 2

It has to do with how microwaves interact with atoms and molecules as opposed to radio waves and infrared radiation. Molecules attempt to align with the electric field that is passing between them and a dipole moment is formed, which comes into contact with other molecules and sends them into motion. This movement creates heat (this mostly occurs in water).