| The Investigation poses questions to generate interest in various mathematical topics from the text and encourages students to formulate and investigate their own conjectures. One use of the investigations is for term papers in which students report on their conjectures and the patterns they find.
Click on the Read Me file below to open the investigation in a Word file:
 Read Me - Areas and Volumes Instructions (Word Format)
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Computer Investigation 10.3Areas and Volumes*
There are many methods for approximating the area of a circle. The ancient Egyptians used a method described in the Rhind Papyrus (1650 B.C.), which involved finding the area of a square that was approximately equal to the area of the circle.
Starting Points for Investigations - The area of a square whose sides are the same as the diameter of a circle is obviously larger than the area of the circle (see figure). Experiment by shrinking the square until both figures have the same area. What percentage of the diameter of the circle can be used as the length of the side of a square so that the area of the square is approximately equal to the area of the circle?
 <![CDATA[<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/free/0072533072/78543/LI_10_3a.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (13.0K)</a>]]>- Extend the method in #1 by using a similar approach to approximate the volume of a sphere by the volume of a cube. Suppose the cube shown below was shrunk until the volume of the cube was approximately equal to the volume of the sphere. What percentage of the diameter of the sphere can be used as the length of the side of the cube so that the volume of the cube is approximately equal to the volume of the sphere?
 <![CDATA[<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/free/0072533072/78543/LI_10_3b.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (20.0K)</a>]]> |
