How many sweat glands are in the Axilla per cm2?
Numbers in the literature vary by a lot. In A Short History of Sweat Glands, Willey et al. compared data from four different studies, the data can be seen in table 1 of the publication. Numbers varied from 68 to over 400 per square centimeter. They explain thus variance by different counting techniques and whether only "active" sweat glands are counted. Also, studies were done on few subjects and only in one gender an ethnicity, which may have quite an impact on this.
The density is highest on the palms and soles, not the armpits, by the way.