. Winslow's Comprehensive mathematics : being an extensive cabinet of numerical, arithmetical, and mathematical facts, tables, data, formulas, and practical . f a spherical segment or zone. Rule. — Multiply the height by the circumference of the sphere. Or, Q = 2-rv = tt (\d2-\-v°), for the segment; r being the radiusof the sphere, d the diameter of the base of the segment, and vilie height; and il =^27rrh = Itt(D2 — d2-\~ 4tf-\-SJw), for the zone; U and dbeing the diameters of the bases, h the height of the cone, and vI lie height of a spherical segment whose base is equal to the les
. Winslow's Comprehensive mathematics : being an extensive cabinet of numerical, arithmetical, and mathematical facts, tables, data, formulas, and practical . f a spherical segment or zone. Rule. — Multiply the height by the circumference of the sphere. Or, Q = 2-rv = tt (\d2-\-v°), for the segment; r being the radiusof the sphere, d the diameter of the base of the segment, and vilie height; and il =^27rrh = Itt(D2 — d2-\~ 4tf-\-SJw), for the zone; U and dbeing the diameters of the bases, h the height of the cone, and vI lie height of a spherical segment whose base is equal to the less use of the zone. 220 MENSURATION OF SOLIDS. To find the solidity of a spherical segment. Rule. — 1. To the square of the height of the segment, add threetimes the square of half the base, and multi-ply the sum by the height, multiplied , and the product is the solidity. Or, — 2. From three limes the axis of thesphere, e f, subtract twice the height of thesegment, and multiply the difference by thesquare of the height, multiplied by .5236,diu\ the product will be the contents. N<b th. V h a d* -f b c2 -i- b c — ef, and e / X ba d~ = h a Example. — The base, a d, of the segment a d c, is 18 inches, andthe altitude, b c, is 8 inches ; required the solidity of the -f 9-X 3 = 307 X 8 X .5236 = cubic inches. Ans To find the solidity of a spherical zone. Rule. — Add the square of the radius of one base to the square ofthe radius of the other, and thereto add £ the square of the height :multiply their sum by the height, multiplied by , and the prod-uct will be the contents. Example. — The base, g h, of the zone g h d o, is 4 feet, the base,a d, is 3 feet, and the height, i b, is 2£ feet; the contents of the zoneare required. -~2 2 = ad. 2- = -i- 3 = =I square of height. Then,~J> -L- = X X = \- cub. feel. Ans. To find the side of the greatest cube that can be cut from a give?i
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