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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?

A rectangular prism and a cylinder have the same height and the same volume What is the length of the side of the prisms square base class=

Respuesta :

[tex]\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}\\\\ [/tex]

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

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