Which explains why the ratio of cell surface area to volume affect the cell size?asap! this is due tomorrow!

Think about it this way: a cell can only take in materials through the cell membrane. Naturally, as the cell membrane surface area increases, then the amount of material that can enter the cell increases due to more entry points along the membrane. However, when the cell increases in size then the volume inside the cell will also increase - more volume inside requires more energy to transport materials around the cell. So, there is a trade-off between the surface area and volume. 
As an example, consider a sphere as a cellular model. The surface area of a sphere is 

SA = 4*pi*r^2 

while the volume of the sphere is 

V = 4/3*pi*r^3 

initially, as a very small cell increases in radius, the surface area will increase at a greater rate than the volume. But as the cell gets bigger there will be a point where the volume increases faster than the surface area. Cells have maximized this ratio through evolution (this is also one reason why we are not single-celled organisms). 
Some cells are able to get around this issue to some extent by "folding" the membrane, thus increasing the surface area without affecting the volume by much. 

They carry out the exchange of gases as we breathe ( oxygen and carbon dioxide).

It idk haha what are we doing?