<P> The fact that the volume of any pyramid , regardless of the shape of the base , whether circular as in the case of a cone , or square as in the case of the Egyptian pyramids , or any other shape , is ( 1 / 3 ) × base × height , can be established by Cavalieri 's principle if one knows only that it is true in one case . One may initially establish it in a single case by partitioning the interior of a triangular prism into three pyramidal components of equal volumes . One may show the equality of those three volumes by means of Cavalieri 's principle . </P>
<P> The fact that the volume of any pyramid , regardless of the shape of the base , whether circular as in the case of a cone , or square as in the case of the Egyptian pyramids , or any other shape , is ( 1 / 3 ) × base × height , can be established by Cavalieri 's principle if one knows only that it is true in one case . One may initially establish it in a single case by partitioning the interior of a triangular prism into three pyramidal components of equal volumes . One may show the equality of those three volumes by means of Cavalieri 's principle . </P>
who calculated the volume of pyramids and cones
who calculated the volume of pyramids and cones
Cavalieri
Cavalieri