. Winslow's Comprehensive mathematics : being an extensive cabinet of numerical, arithmetical, and mathematical facts, tables, data, formulas, and practical . e of a Frustum of a Pyramid, Frustum ofa Cone, Prismoid, or Wedge. Rule. â Multiply the sum of the perimeters of the bases by halfthe slant height. Example. â Each edge of one of the bases of the frustum of ahexagonal pyramid is 4 feet; each edge of the other base, 2 feet jand the slant height of the frustum is 24 feet: required its lateralsurface. 4 X 0 + 2X 6 X ~f == 432 square feet. Ans. To find the solidity of the frustum of
. Winslow's Comprehensive mathematics : being an extensive cabinet of numerical, arithmetical, and mathematical facts, tables, data, formulas, and practical . e of a Frustum of a Pyramid, Frustum ofa Cone, Prismoid, or Wedge. Rule. â Multiply the sum of the perimeters of the bases by halfthe slant height. Example. â Each edge of one of the bases of the frustum of ahexagonal pyramid is 4 feet; each edge of the other base, 2 feet jand the slant height of the frustum is 24 feet: required its lateralsurface. 4 X 0 + 2X 6 X ~f == 432 square feet. Ans. To find the solidity of the frustum of a â To the square root of the product of the areasof the bases, add the areas of the bases, and multiplythe sum by £ the perpendicular height of the frustum ;*the product will be the solidity. Example.âThe greater base of the frustum of aquadrilateral pyramid is 3 feet on each side, and the lessbase is 2 feet on each side, the perpendicular height ofthe frustum is 15 feet; what are its solid contents? 3X3 = 9 feet = area of greater base. 2X2 = 4 feet = area of less base. 15-=- 3 = 5= £ height. Then, 0X4 = V36 = 6 + 9 + 4=19X5 = 95 Ans. OF PRISMOIDS AND THE find the solidity of a prismoid. The Rule for finding the solidity of the frustum of a pyramid isequally applicable to the prismoid. Or, Rule. â Add the areas of the ends, and four times the area of themean between the ends, together, and multiply the sum by ^ the per-pendicular height; the product will be the capacity or solidity. Example.âThe bottom of a rectangular cistern is 8 feet by 0feet, the top is 4 by 3 feet, and the perpendicular depth is 12 feet;required its capacity. a .o 4 .3 -j- 2 = 0 X = 27 X 4 = 108 = 4 area of mean ; and6 X 8 -f 4 X 3 = 00 -f- 108 = 108 X -^ = 330 cubic feet. Ans. *For another rule, see Mensuration of Prismoids MENSURATION OF SOLIDS 217 To find (fie solidity of a âMultiply the sum of the length ofthe edge and twice the length of
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