Answer
$$\frac{15\pi }{2}$$
Work Step by Step
Given $$x=\sqrt{y},\ \ \ y\in [1,4] $$
Then the volume of the solid obtained by rotating the region enclosed by the graph of
$ x=\sqrt{y}$ about the $y-$axis is given by
\begin{align*}
V&=\pi\int_{1}^{4}[f(y)]^2dy\\
&= \pi \int_{1}^{4}ydy\\
&=\frac{\pi}{2}y^2\bigg|_{1}^{4}\\
&=\frac{15\pi }{2}
\end{align*}
We use the Mathematica program to plot the solid.