Orders of Magnitude: How many grains of sand in a wine glass? Am I correct

Hey everyone! I'm supposed to approximate how many grains of sand can fit in a wine glass. Please tell me if my steps are correct.
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Average wine glass= 8 fluid ounces.
=236.588237 cm^3 = Volume of Wine Glass = 2.369 x 10^9 mm^3

Volume of Grain of Sand=
diameter= .05 mm
Volume= 6.55 x 10^-5 mm^3

How many gains of sand in 1 mm^3?
1 mm^3 / (6.55 x 10^-5) = 15,267. 176 grains of sand

How many grains in the wine glass?

(2.3659 x 10^9 mm^3) x (15,267.176) = 3.6 x 10^13
because I'm looking for the order of magnitude, I shall discard the 3.6 and allow 10^14 to suffice.

Answer: 10^14


IS THIS CORRECT? It doesn't seem like enough grains to me :/

Just go with powers of ten

Volume of glass 236 cm^3 = 2.37 x 10^5 mm^3 (there are 10 mm in a cm !!) = 10^5

Volume of one grain is correct so in one mm^3 there are 1.5 x 10^4 call it 10^4

so in volume 10^4 there are 10^4 x 10^5 = 10^9 grains of sand.

How many gains of sand in 1 mm^3?
1 mm^3 / (6.55 x 10^-5) = 15,267. 176 grains of sand

15,000 grains of sand in a mm cube ?
that sounds pretty high, just intuitively ... sounds more like powder than sand grains

looks good to me