We measure angles on paper, in two dimensions, in either degrees or radians but when we need to deal with three dimensions, for example when something spreads out like a cone, then the unit used is a steradian. The video below illustrates and explains exactly what a steradian is.

The total surface area of a sphere = 4πr²

so by this definition the total solid angle subtended at the centre of a sphere must be:

4πr² /r²

the r²  cancel out, which equals 4π steradians that is 4π sr