Question

A rectangular prism and a cylinder have the same height and the same volume. What is the length of the side of the prism's square base?

Answer 1

$\bf \textit{volume of a cylinder}=V_c=\pi r^2 h\qquad \begin{cases} r=radius=\frac{diameter}{2}\\ h=height\\ ----------\\ diameter=8\\ radius=\frac{diameter}{2}=4 \end{cases} \\\\\\ V_c=\boxed{\pi 4^2 h} \\\\\\ \textit{volume of a rectangular prism}=V_p=lwh\qquad \begin{cases} l=length\\ h=height\\ w=width\\ -------\\ length=x\\ width=x \end{cases} \\\\\\ V_p=xxh\implies V_p=\boxed{x^2h}$

$\bf -----------------------------\\\\ \textit{now, we know that their volumes and height are equal} \\\\\\ thus \\\\\\ \pi 4^2 h=x^2h$

solve for "x"