Pyramids, Cones
The regular or right cone has a circle for its base that is perpendicular to its height.
The regular or right pyramid has some regular polygon for its base that is perpendicular to its height.
The formulae for all regular polygons and the circle is the same herein, and only the ratio of pi is varied to match the appropriate polygon. Thus the bases of cones and pyramids are calculated the same way for area and circumference.
The regular cone and pyramid has a volume 1/3 of a bar, rod, column, or prism with the same respective base and equal height. Thus the volume is calculated with a like formulae of base area times height... as for a cylinder__ except now, with the cone and pyramid... it is divided by three.
Note: Here, with cones and pyramids, the centerline is the height as with bars, rods and columns... radii is poly radii.
The total surface area for a cone or pyramid is the base area, Ab, plus the Lateral area, A1.
Poly pi times poly radii will result in one half the circumference of the base of any cone or pyramid. One half the base circumference times the slant height, S, will result in the area of the lateral surface, A1. Refer back to Figure 6 and 7 of the Area web page. This lateral area is done by using multiple triangle pie slices. But, instead of r times C and dividing by two__ we multiply poly pi times r (instead of d), which gives immediately one half circumference, and then simply multiply times the lateral slant height line, S, for lateral surface area. Thus more continued similarity of polygons and circles... And similarities with bars, rods, cylinders, columns, and prisms...
V = (Ab h) / 3
Al = ¶x r S or Al = (CS/2)
(C = Circumference of the base polygon)
