Chemistry problem with volumes - help!

Ooh interesting, although that is a very low conc.
First the volume for a sphere = 4pi/3 r ^3
You would need the volume to be 1.67 x 10^36 dm^3 for there to be one mole there which is 1.67 x 10^33 m^3 (that is riduclousy large about a million x the size of the sun)
So the radius of a sphere for a given volume is given by (3/4pi V)^1/3 which would make the radius about 7.36 x 10 ^10 m or 73600000 km (about the distance to mars)
This questions seems a non-sequitir are you sure the conc is correct?

1/(6 x 10^-37) dm^3 = volume of substance for 1 mole of substance = volume of sphere = 1.67 x 10^36
volume of sphere = 4/3 pi r^3
1.67 x 10^36 = 4/3 pi r^3
pi r^3 = 1.67 x 10^36 x 3/4 = 1.25 x 10^36
r^3 = (1.25 x 10^36)/pi = 4 x 10^35
r = 7.36 x 10^11 dm
= 7.36 x 10^9 m
= 7.36 Gm

Y'know, I got that answer, too, but apparently you should get 1.46 x 10^11m

It's not for an exam question or anything. I was trying to work out the size a spherical pill would have to be to contain one molecule of the original substance based on a 30C dilution (homeopathy stuff, if you are unfamiliar), and just compare it with something.

There are 10 dm in a meter

Hmm I don't see how you would get that...
Not a big fan or have that much knowledge on the alternative medicines