What problem aries due to the fact that the rate of volume growth is faster than surface area growth?

When the volume growth is faster than the SA growth than things start to get dangerous.

Lets put it this way. 

say you're filling yourself with air like a balloon

however your growing to fast and your skin cannot stretch fast enough and you pretty much blow up.

think of someone just filling themselves with air and it's already too silly for you not to remember