ANSWERS: 4
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Just a guess, but your hands and feet are constantly in contact with other things and air so the sweat is distributed almost as fast as it is produced. Your head is likely covered with hair that blocks the cooling breeze that would help evaporate the sweat.
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I don't know if the question is correct in its assumption, but if this is true or even remotely close, it may be because: of the constantly circulating blood (very little of which is ultimately filtered to sweat by glands), about _25% goes to the head_, while normally only about 6% goes to _all_ of the skin. When we work out, or "flush" that 6% comes closer to 20%, but that's to all skin, not just palms, soles, and armpits, and there's alot of skin. Hypothetically, a good reason for humans still having head hair is to prevent excessive heat loss through the head, considering so much arterial blood fluxes through such little volume per heartbeat. I guess the lesson is: primate brains are very demanding.
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It is easier to cool down via perspiration through your head because: (1) it is a very well-vasculated area, and blood carries a lot of the body's heat; (2) the head is most likely to be in contact with the atmosphere - a cool breeze is more likely to get to your head and cool you down through evaporation of your sweat than it is to get to your feet in their socks and shoes; (3) because of point (2), your head has the largest surface area exposed to the external environment, and is therefore the most efficient heat-reducing method available to you.
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I haven't read this anywhere, but just thinking about your question gave me an answer. Your are right in that there are more sweat glands located in the thick epidermis located on the palms of the hands and the bottoms of your feet. Gray's Anatomy gives specifics and the palms have about twice the density of sweat glands as the forehead. I think the answer is because of the volume to surface area ratio of the different parts of the body. Basically a thick apendage conserves heat better. A thin finger gets cold faster than your head. And vice versa, your head gets hot faster than your fingers. The same with toes and feet. That is why when people get frost bite on their feet it's the toes that get frost bitten first. Your head sweats more than your palms because it's not as efficient at shedding heat. This is also why cold environment organisms tend to be big. For example polar bears and seals. The volume to surface area ratio is lower in larger animals. Big is better in cold environments.
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