Plane and solid geometry . Fig. Given prismatoid CF with its volume denoted by F, its lowerbase by B^ its upper base by 6, its altitude by H, and a sectionmidway between the bases by M. To derive a formula for V in terms of B, b, H, and M, If any lateral face as AD is a trapezoid, divide it into two Aby diagonal AD, intersecting NK at L. Let P be any point in M and join it to all vertices of theprismatoid. This will divide the prismatoid into pyramidshaving their vertices at P and having fcr their bases B, b, andthe triangles forming the lateral faces of the prismatoid. The volume of pyram
Plane and solid geometry . Fig. Given prismatoid CF with its volume denoted by F, its lowerbase by B^ its upper base by 6, its altitude by H, and a sectionmidway between the bases by M. To derive a formula for V in terms of B, b, H, and M, If any lateral face as AD is a trapezoid, divide it into two Aby diagonal AD, intersecting NK at L. Let P be any point in M and join it to all vertices of theprismatoid. This will divide the prismatoid into pyramidshaving their vertices at P and having fcr their bases B, b, andthe triangles forming the lateral faces of the prismatoid. The volume of pyramid P-B = \ B - \ H = \ H - B] and thevolume of pyramid P-b = ^ b - ^ H = ^^ H-b. § 805, Consider pyramid P-ADC. Draw PK, PL, and LC (Fig. 2).This divides pyramid P-ADC into three pyramids, D-KLP,C-KLP, and P-ALC. Denote A KLP by iiij. Then volume of pyramid D-KLP = ^ H* tUi] and the vol-ume of pyramid C-KLP = ^ Hmi. § 805. Pyramid P-ALC A ALC u . A ALC AC 2 -^ = ; but = —=-. LK 1 Pyramid P-CLK { C-KLP) A CLK A CLE .*. pyram
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Keywords: ., bookcentury1900, bookdecade1910, booksubjectgeometr, bookyear1912
