Accepted answer
It gives 7.5 mg/mL, and whether that is sensible depends on the dose you will draw from it. 15 ÷ 2 = 7.5 mg/mL in phosphate-buffered diluent. A 0.5 mg dose is then 6.7 units on a U-100 barrel and a 1 mg dose is 13.3 units. Both land in a readable part of the barrel, which is the whole point of choosing the volume deliberately.
Answer first: diluent volume sets concentration and therefore resolution on the syringe barrel, and resolution is free at reconstitution and impossible to recover afterwards.
Content matters. If the same 10 mg vial assays at 94 per cent content, you have 9.4 mg. In 2 mL that is 4.7 mg/mL, and a nominal 0.5 mg draw of 10 units actually delivers 0.47 mg — a six per cent shortfall that no amount of careful drawing will fix.
The other direction: 10 mg in 3 mL is 3.33 mg/mL, and a 0.5 mg dose becomes 0.15 mL, or 15 units. More barrel, easier reading, and a larger fraction of the vial volume lost to dead space across the same number of draws.
U-100 means 100 units per millilitre by definition, so 1 unit is 0.01 mL and volume in millilitres times one hundred gives units. Every conversion here reduces to that.
Choose the volume that puts your largest intended dose between 10 and 30 units. Everything else follows.