Mathematics

The key is recognizing which curve is on top, then using the washer method — subtracting the inner disk from the outer disk at each slice perpendicular to the axis of rotation. Find where $\sqrt{x}$ and $\frac{x}{2}$ intersect to set your integration bounds, then integrate $\pi(R^2 - r^2)$ with respect to $x$, where $R$ and $r$ are the outer and inner radii.

The key is recognizing which curve is on top, then using the washer method — subtracting the inner disk from the outer disk at each slice perpendicular to the axis of rotation. Find where $\sqrt{x}$ and $\frac{x}{2}$ intersect to set your integration bounds, then integrate $\pi(R^2 - r^2)$ with respect to $x$, where $R$ and $r$ are the outer and inner radii.