+743 Let $\mathcal{R}$ be the circle centered at $(0,0)$ with radius $15.$ The lines $x = 8$ and $y = 1$ divide $\mathcal{R}$ into four regions $\mathcal{R}_1$, $\mathcal{R}_2$, $\mathcal{R}_3$, and $\mathcal{R}_4$. Let $[\mathcal{R}_i]$ denote the area of region $\mathcal{R}_i$. If
\[[\mathcal{R}_1] > [\mathcal{R}_2] > [\mathcal{R}_3] > [\mathcal{R}_4],\]
then find $[\mathcal{R}_1] + [\mathcal{R}_2] + [\mathcal{R}_3] + [\mathcal{R}_4]$.
