I am having a very basic confusion on how we calculate the height of atmosphere when we assume that the density does not change with altitude(density remains 1.29 kg/m$^3$).
I want to know why we say that in this case that the atmospheric pressure is $$P=\rho gh$$
I think my confusion here is if there is any pressure exerted on the atmosphere itself!
Because we can say in this question that $$ P_{\text{on the atmosphere}}-P_{\text{by the atmosphere}}=\rho gh $$
Then if pressure on the atmosphere is 0 then my confusion is gone :) Otherwise please explain the same.
By the way the answer to the above question is about 8Kms.