Assume that the density of the atmosphere as a function of altitude h (in kilometers) above sea level is δ(h) = ae^−bh kg/km³, where a = 1.225 × 10⁹ and b = 0.13. Calculate the total mass of the atmosphere contained in the cone-shaped region x² + y² ≤ h ≤ 3.

Assume that the density of the atmosphere as a function of altitude $h$ (in kilometers) above sea level is $\delta \left(h\right)=a{e}^{-bh}kg/{km}^3$, where $a=1.225\times {10}^9$ and $b=0.13$. Calculate the total mass of the atmosphere contained in the cone-shaped region $\sqrt{x^2+y^2}\le h\le 3$.