Answer
$\text{The volume is}$
\begin{align}
V = \frac{32}{5}
\end{align}
Work Step by Step
$\text{It is given that}$
\begin{align}
f(x) = x^2; x = 0 \ and \ x = 2
\end{align}
$\text{To find the volume, we have to find the area of the cross section.}$
$\text{It is given that the cross section is squre, therefore:}$
\begin{align}
A(x) = f^2(x)
\end{align}
$\text{Thus, the volume is}$
\begin{align}
V = \int_0^2 x^4 \ dx = \left[ \frac{x^5}{5} \right]_0^2 = \frac{32}{5}
\end{align}
