Question

How how the minimum body surface area help to reduce heat loss from the body of the polar bear

Answer 1

Compared to other species of bears, polar bears have small extremities, proportionally shorter legs and a stockier build. This reduces the surface area to lose heat from. This is a common characteristic amongst animals that live in cold environments that enables them to retain their heat and conversely means they often can't cope with warm temperatures as they easily overheat in warmer temperatures.

Small extremities to reduce heat loss (anatomical) - Polar bears have small ears covered in thick fur, a very short tail and a relatively short and squat muzzle, all of which help to retain heat.

Polar bears eat a very high fat diet and have adaptations to allow them to process this food (physiological) - *This is possibly the key adaptation that polar bears have*. It enables them to eat the blubber of the seals that they catch which is the most energy rich and abundant part of the seal. Other animals could simply not survive if they ate so much fat in their diet. Adult bears often only eat the blubber while younger still growing bears will also eat the meat for protein.

Thick layer of body fat / blubber (anatomical / physiological) - This can be up 10cm (4 inches) thick, it is used both for insulation and also for food storage to help survive when food supply may be intermittent especially in the summer months when bears often go hungry for long periods due to not being able to hunt their preferred food of seals. Up to 50% of a polar bears weight can be fat! It also helps they to float naturally when swimming so avoiding having to use energy to keep their head out of the water.
Processing body fat to gain metabolic water (physiological) - Polar bears store a lot of fat which they use for energy in the process combining it with oxygen to release carbon dioxide and metabolic water. They live in a polar desert with little access to fresh water especially in the colder months (which are in the majority) in this way they can get extra fresh water - camels do a similar thing with their stored fat.

Thick camouflaged fur (anatomical) - The coat of the polar bear is especially thick and luxurious being the thickest of any bear (unsurprisingly!). There are two kinds of hairs, short soft dense inner hairs and longer stiffer outer guard hairs. The coat is the same colour all year round unlike some arctic animals which have a darker coat in the summer months. The coat usually appears to be perfectly white, though has a pale yellow tinge to it which becomes more pronounced in older animals. The colour of course provides camouflage against an icy and snowy background.

Thick fur on the paws (anatomical) - to insulate them from snow and ice and also provide for grip on slippery surfaces. The paws are large in size to help spread the bears weight over ice and snow and have blubber under the pads for extra insulation.