Shape 

Copyright David & Cynthia Thomas, 2009

Surface Area and Volume--Challenge: Folding the Circle

Print out the circle found in the appendix to this chapter.  Then follow the directions in Table 6.8.  Answer the questions asked in the table. 

	Cut away the paper outside the circle, leaving a paper disc.  Find the center of the circle by folding two diameters and noting their intersection.  1. Why does this procedure identify the center of the circle? Fold a random point on the circle to the center as shown.
	Perform two additional folds as shown. 2. What sort of triangle is created? 3. Why does this procedure “work”?
	Fold each vertex to the center of the opposite side and crease the paper as shown. 4. Assume that the large triangle has an area of 1 unit^2. What is the area of each of the smaller triangles?  Why?
	Fold up the corner triangles to create a regular tetrahedron.  5. What is the surface area of the tetrahedron?  Why?
	Unfold the tetrahedron.   Then fold the outside vertex of each large corner triangle to the midpoint of its opposite side. 6. What is the area of each small triangle formed in this manner?  Why?
	Fold up the large corner triangles and overlap the small corner triangles to create the truncated tetrahedron shown at the left. 7. What is the surface area of the truncated tetrahedron?   Why? 8. What fraction of the tetrahedron’s total volume was lost in the truncation?  Why? 9. What fraction of the tetrahedron’s total volume remains?  Why?

Table 6.8: Folding the Circle