Is it necessary for a women to cover her hair or is it more necessary for her to cover her body.

Answer:
When in the presence of her 'mehrams', it is not necessary for the believing woman to cover her hair; but when in the presence of 'non-mehrams', the believing woman is commanded to and it is absolutely obligatory for her to cover her full body (including her hair), except her face and her hands. And Allah alone knows the best.