How many hairs on a reindeer?

When we visited the Cairngorm reindeer, I was given a figure of 2000 hairs per square inch. If we say that a reindeer is modelled by a cylinder 3 feet long and 1 foot diameter, surface area is pi^2 x radiius x length = pi^2 x  36 = 2131 square inches. That would mean 4.25 million hairs.That's more than I was expecting!