Q1: The fundamental equation of air content (a_c), degree of saturation (S_r) and void ratio (e), is

ANS:C - a_c =

We know that vol Of voids = vol Of air + vol Of water.

Dividing both sides with vol Of voids then we get air content + degree of Saturation = 1. The percentage of air voids should be on LHS which is equal to porosity*air content, air content is equal to 1-S, porosity = e/1+e. Actually here is not air content, here is air voids.
ac+Sr=1, ac=1-Sr.
Na=ac*n, n=e/1+e.
Na=e(1-Sr)/(1+e).