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Take a Slice
Cross Sections of Solids
Introduction
What would happen if you sliced through the center of a
baseball? The sliced shape would be a
circle. If you sliced through the ball
on a line away from the center, you would see a smaller circle than the
original. Find out what happens when
you slice through various solids.
Task
Use modeling clay or playdough to examine the slice of a
right circular cylinder, a cone, a cube, a triangular, prism, a square pyramid,
and a solid of your own choice.
Make a poster, transparency, or power point with drawings of
your solids and the tracings of the shapes made by the cross sections to
present to the class.
Give a brief demonstration with the clay models on how the
cross sections were made.
Process
I.
Roll a piece of modeling clay on a
table to form a thick tube. Then use
dental floss or a piece of thread to cut off the ends. Slice the sides perpendicular to the sides
of the tube. You have just created a
cylinder.
II.
Use the string to slice through the
cylinder horizontally as shown on the right.
Place
the cut surface on a piece of paper and
trace around it. What shape do you get?
III.
Reconstruct
the cylinder. Use string to slice the
cylinder on an angle as shown at the right. Place the cut surface on a piece of
paper and trace around it. 
What
shape do you get?
IV.
Reconstruct
the cylinder. Use string to slice the cylinder vertically as shown oat the
right. Place the cut surface on a 
piece
of paper and trace around it.
What shape do you
get?
V.
Use modeling clay to form a cone. If this is difficult, use a piece of
posterboard and tape to form a cone-shaped mold. Then pack the clay tightly into the mold and pop out or cut the
tape to form the cone.
VI.
Use the string to slice through the cone as shown in
each diagram. Place the cut surface on
a piece of paper and trace around it.
Identify the shape determined by each cross section. Remember to reconstruct the cone after each
slice.
VII. Use the resources below to explore the mathematics and
applications of cross sections.
Resources
Evaluation
Conclusion
Now that you have seen the practical applications of cross
sections, you will appreciate them more when you go on to higher mathematics
courses. If you can find other
applications besides the links above, include them in your presentation.