A region $R$ is bounded above by the graph of the parabola $y=1-x^2$ and below by the $x$-axis.
![](web+graphie://ka-perseus-graphie.s3.amazonaws.com/0e8cc952361a631092f9ef0044035243a3add425)
Rotating region $R$ about the vertical line $x=1$ generates a solid of revolution with volume $V$.
**Enter the exact value of the volume as $\pi$ times a fraction.**
**$V=$** [[☃ expression 1]]