Let $S_1=(x,y)|{\log }_{10}(1+x^2+y^2)\le 1+{\log }_{10}(x+y)$ and $S_2=(x,y)|{\log }_{10}(100+x^2+y^2)\le 2+{\log }_{10}(x+y)$. What is the ratio of the area of $S_2$ to the area of $S_1$?