So it is crucial in living things that rely on diffusion to deliver oxygen for respiration, that the SA is large in proportion to size.
In bigger organisms the ratio reduces so that the SA is not big enough to allow for diffusion to supply the whole organism with oxygen. In addition to this the diffusion distance is larger and so it would take a long time for gas exchange to take place via diffusion.
To overcome this large organisms develop systems for gas exchange, for example lungs and gills. These systems will have a large surface area allowing for quick diffusion.
Other animals change their shape to increase their surface area, for example Flat-worms have a flat shape.
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