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6.7 Something More Solid > 6.7 Something More Solid - Pg. 126

126 CHAPTER 6 1 2 2 1 1 1 3 E 2 2 F' E' B F G H J 3 D G' H' C Figure 6.10. The net of a yángm . a A B A B F E D A F E D J C D B G H C F E J D G' H' C A F' E' D B G H C C A B G Figure 6.11. The construction steps for a yángm . a 3. Make a fold FG so that AB is perpendicular to AD through E. 4. Fold EH, parallel to DC. Where EH intersects AC mark on J. 5. Fold the two lines E H and F G , both parallel to AD, as shown in the bottom right of figure 6.11. Since three identical yángm make a cube, their volume is one- a third that of the cube. This result is actually considerably more general: the volume of any straight-sided pyramid is one-third of the base area multiplied by the vertical height. In chapter 8 we consider area in detail, and illustrate why the area of a circle 1 is r 2 . Hence the volume of a circular cone must be r 2 3 h.