Find the volume of the solid obtained by rotating the region bounded by $y=\sqrt{x}$, the $x$-axis and the vertical lines $x=0$ and $x=4$ about the $x$-axis using the washer (disk) method.

Step-by-step solution

1. For rotation about the $x$-axis, each cross‑section perpendicular to the $x$-axis is a disk of radius $y=\sqrt{x}$.
2. Area of a typical disk: $A(x)=\pi y^2=\pi (\sqrt{x}{)}^2=\pi x$.
3. Volume $V={\int }_0^{4}A(x)dx=\pi {\int }_0^{4}xdx$.
4. Integrate: $\pi {\left[\frac{x^2}{2}\right]}_0^4=\pi \times \frac{16}{2}=8\pi$.

Concept tested: Volume by washer method

Published 14 September 2026 · Last updated 16 September 2026 · How this solution was prepared and checked