Chapter 6.2, Problem 27ES

True-False Determine whether the statement is true or false. Explain your answer. [In these exercises, assume that a solid $S$ of volume $V$ is bounded by two parallel planes perpendicular to the $x\text{-axis}$ at $x=a$ and $x=b$ and that for each $x$ in $\left[a,b\right],A\left(x\right)$ denotes the cross-sectional area of $S$ perpendicular to the $x\text{-axis}$ .]

If each cross section of $S$ perpendicular to the $x\text{-axis}$ is a square, then $S$ is a rectangular parallelepiped (i.e., is box shaped).