artery, vein, or capillary that has the greatest total cross-sectional area
The total cross-sectional area of the capillaries is the greatest; that's why the blood velocity is the slowest through capillaries (this is very important since this is the site of nutrient exchange and you want blood to slow down to allow proper exchange rather than rush past).apillaries have the most area. Its pretty simple. Capillaries carry blood to every cell in the body. Obviously they have the biggest surface area.