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\begin{document}

\noindent
{\Large 
Measurement Worksheet III \hfill Name:\underline{\hspace{2.8in}}\\ \\
MA~202 \\
Spring Semester 2004}
\vspace{.25in}

\noindent
{\bf WARNING:}  You must {\bf SHOW ALL OF YOUR WORK}.  You will receive 
NO CREDIT if you do not show your work.

\noindent
{\bf DUE:} {\bf ????} 
\begin{enumerate} 
\item You should be able to do problems similar to numbers 1--5
and 12--13 in Section 12.3 of your textbook.  I will not collect these
problems.
\item Do problem 4c in Section 12.3 of your textbook. ({\bf HINT:}{\em What
is the radius of the sphere?  Draw a radius that is not labeled.})
\item Do problems 6--9, 10a, 14, and 15 in Section 12.3 of your textbook.
\item Do problem 25 in Section 12.3 of your textbook.
\item Read Section 12.4 of your textbook.
\item 
	\begin{enumerate}
	\item Draw four different nets for the Polydron cube you are given.  
	\item Use the nets to find the surface area of the cube.
	\item Use the net to verify that the surface area of the cube is
	\[(2
	\times \text{ area of the base }) + (\text{ perimeter of the base }
	\times \text{ height of the cube}).\]
	\end{enumerate}
\item 
	\begin{enumerate}
	\item Draw two nets for a the Polydron rectangular prism (which is not
	a cube) you are given.  
	(Could you draw more nets for this rectangular prism?)
	\item Use the nets to verify that the surface area of this
	rectangular prism is \[(2
	\times \text{ area of the base }) + (\text{ perimeter of the base }
	\times \text{ height of the prism}).\]
	\end{enumerate}
\item 
	\begin{enumerate}
	\item Draw two net for a the Polydron triangular prism you are given.  
	(Could you draw more nets for this triangular prism?)
	\item Use the nets to verify that the surface area of this
	triangular prism is \[(2
	\times \text{ area of the base }) + (\text{ perimeter of the base }
	\times \text{ height of the prism}).\]
	\end{enumerate}
\item 
	\begin{enumerate}
	\item Use Polydron to construct a tetrahedron.
	\item Draw a net for your tetrahedron. (Could you draw more than
	one net for this tetrahedron?)
	\item Use the net to find the surface are area of your tetrahedron.
	\end{enumerate}
\item Consider the cylinder and the sphere in your set of Power Solids or
Relational GeoSolids.  
	\begin{enumerate}
	\item How does the diameter of the cylinder compare with the diameter
	of the sphere?
	\item How does the height of the cylinder compare with the diameter of
	the sphere?
	\item Fill the sphere with rice.  Dump this rice into the cylinder.
	Compare the volumes of the cylinder and the sphere.
	\end{enumerate}
\item Consider the cube and the pyramid with the square base
in your set of Power Solids or Relational GeoSolids.  
	\begin{enumerate}
	\item How does the base of the pyramid compare with the base of the
	cube?
	\item How does the height of the pyramid compare with the height of
	the cube?
	\item Fill the pyramid with rice.  Dump this rice into the cube.
	Compare the volumes of the pyramid and and cube.
	\end{enumerate}
\item Consider the cylinder and the cone in your set of Power Solids or
Relational GeoSolids.  
	\begin{enumerate}
	\item How does the diameter of the base of the cone compare with the
	diameter of the cylinder? 
	\item How does the height of the cone compare with the height of
	the cylinder? 
	\item Fill the cone with rice.  Dump this rice into the cylinder.
	Compare the volumes of the cone and the cylinder.
	\end{enumerate}
\item There are three patterns given in problem 10 of Section 11.3.  Use
multilink cubes to construct the three objects that correspond the
patterns.  Find the surface area and volume of each object.
\item Construct various objects using eight multilink cubes.  Which object
has the minimum surface area?  The maximum surface area?  The minimum
volume?  the maximum volume?
\item Construct various objects using six multilink cubes.  Which object
has the minimum surface area?  The maximum surface area?  The minimum
volume?  the maximum volume?
\item 
	\begin{enumerate}
	\item Do problem 5 from section 12.1.  
	\item Replace the word ``volume'' with the phrase ``surface area''
	in problem number 5 of Section 12.1 and repeat the exercise.
	\end{enumerate}
\item Do problems 1--5, 6,7, 10, 11, and 13--15 in Section 12.4.
\end{enumerate}
\end{document}
