Okay so this question comes in two parts and the second part of the question doesn't make any sense to me.
Let $R$ be the region in the first quadrant that lives between the curves $f(x) = x^2$ and
$g(x)=\sqrt{x}$
$(a)$ Sketch $R$ and determine its $area$.
I did this getting $\frac13$ as my area
$(b)$ Now suppose that $R$ is the base of a solid. For this solid, each cross section perpendicular to the $x-axis$ is a square. Find the $volume$ of this solid.
How to do this?
It looks something like this...
So the length of the square at $x$ is $h=\sqrt{x}-x^2$, and the area is $A=h^2$. Now integrate $A\,\mathrm{d}x$ along $x$ to find the volume.