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%TCIDATA{<META NAME="Title" CONTENT="Reference/Mathematics/Rectangular Parallelopiped">}
%TCIDATA{Created=Mon Aug 19 14:52:24 1996}
%TCIDATA{LastRevised=Sun Mar 30 14:27:08 1997}
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\section{Rectangular Parallelopiped\label{Rectangular parallelopiped}}

\begin{definition}
A \textbf{rectangular parallelopiped} (or \textbf{box}) is a closed
geometric figure with six sides, in which each side is a rectangular plane
segment, opposite sides are parallel, and all interior angles are right
angles. A \textbf{cube} is a rectangular parallelopiped in which all sides
are equal\medskip .
\end{definition}

\subsubsection{\textbf{Box\label{Box}}}

Let $l=$ length, $w=$ width, and $h=$ height.\FRAME{dtbpF}{147.3125pt}{%
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\begin{itemize}
\item  The \label{Surface area of box}\textbf{surface area} of a box is the
sum of the areas of the sides.

$S=2lw+2lh+2wh$

\item  The \label{Volume of box}\textbf{volume} of a box is the length times
the width times the height.

$V=lwh$

\item  The \label{Diagonal of box}\textbf{diagonal} of a box is the square
root of the sum of the square of the length, width, and height.

$d=\sqrt{l^{2}+w^{2}+h^{2}}$
\end{itemize}

\begin{example}
If a box has length $l=10$, width $w=6$ and height $h=5$ then the surface
area, volume, and diagonal are 
\begin{eqnarray*}
S &=&2\times \left( 10\times 6\right) +2\times \left( 10\times 5\right)
+2\times \left( 5\times 6\right) =280 \\
V &=&10\times 6\times 5=300 \\
d &=&\sqrt{10^{2}+6^{2}+5^{2}}=\sqrt{161}\approx 12.\,\allowbreak 689
\end{eqnarray*}
\end{example}

\subsection{\ Related Reference Topics}

{\small \hyperref{Table of Geometric Formulas For Length, Area, and Volume}{%
}{}{TAB_geom_formulas.tex}}

{\small \hyperref{Trigonometry}{}{}{TR_contents.tex}}

\subsection{\ Related Scientific Notebook Topics}

{\small \hyperref{Angular Measure}{}{}{../../Help/DMIndex.tex#Angular measure%
}}

{\small \hyperref{Conic Sections}{}{}{../../Help/DMIndex.tex#Conic sections}}

{\small \hyperref{Plotting Curves and Surfaces}{}{}{../../Help/DM6.tex}}

{\small \hyperref{Polygons}{}{}{../../Help/DMIndex.tex#Polygons}}

{\small \hyperref{Surfaces of Revolution}{}{}{%
../../Help/DMIndex.tex#Surfaces of revolution}}

{\small \hyperref{Trigonometry}{}{}{../../Help/DM4.tex}}

{\small \hyperref{Volume of parallelpiped}{}{}{%
../../Help/DM9-1.tex#Parallelpiped}}\hfill 

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