Your friend of mass 150kg can just barely float in fresh water .calculate her approximate volume. express your answer to two significant figures and include the appropriate units.

The mind boggles at the spectacle ... a 150-kg lady weighs about 330 pounds, and has the courage and the audacity to not only go to the beach, but to go out and float in the water, hoping that there are no wise little kids around, getting ready to yell to each other "Thar she blows, Cap'n !".

But we're only here to do the math, whether or not it has any physical significance in the real world.

This problem is really not that mysterious. 

Since the star of this unlikely scenario is just barely floating, her weight must be equal to the weight of an equal volume of water.  In other words, her average density  (arrghhh, I can't take much more of this) is equal to the density of water.

Officially, 1 kg is the mass of fresh water that occupies a volume of 1 liter, so this relationship also very nearly describes the relationship between our heroine's mass and volume.

Her volume is very nearly 150 liters, or  0.15 cubic meter, and no further rounding is necessary, in more ways than one. 

I would stay and convert that to some more familiar 'customary' units for you, honest I would.  But I've been quite overcome by my visualizations of this whole matter, and I really must make a quick trip to the rail, immediately.