. Winslow's Comprehensive mathematics : being an extensive cabinet of numerical, arithmetical, and mathematical facts, tables, data, formulas, and practical . -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 — Divide the square of the diameter of the sphere by 3, andthe square root of the quotient is the side; or, multiply the diameterof the sphere by .57735, and the product is the side. Example.—The diameter of a globe is 15 inches; required thes
. Winslow's Comprehensive mathematics : being an extensive cabinet of numerical, arithmetical, and mathematical facts, tables, data, formulas, and practical . -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 — Divide the square of the diameter of the sphere by 3, andthe square root of the quotient is the side; or, multiply the diameterof the sphere by .57735, and the product is the side. Example.—The diameter of a globe is 15 inches; required theside cf the greatest cube that may be cut from the X 15 = 225 -T- 3 = V75 = inches, or15 X .57735 = inches. Ans. MENSURATION OF SOLIDS. 221 OF find the solidity of a — Multiply the square of therevolving axis by the fixed axis multi-plied by .5236, and the product is thesolidity. Example. — The fixed axis, a b, of the prolate spheroid ac b d, is 32 inches, and the revolving axis, erf, is20 inches ; required the solid contents. 202 X 2 X .5236 = cubic inches = -j- 1728 = cubic feet. To find the solidity of the segment of a spheroid. Rule. —When the base of the segment is parallel to the shorter axisof the spheroid.—From three times the length of the longer axis,subtract twice the height of the segment, and multiply the differenceby the square of the height, multiplied by the square of the shorteraxis, multiplied by .5236, and divide the product by the square of thelonger axis ; the quotient will be the solid contents of the segment. Rule. — When the base of the segment is parallel to the longer axisof the spheroid. — From three times the length of the shorter axissubtract twice the height of the segment, and multiply the differenceby the square of the height multiplied by the longer axis, multipliedby .5236, and divide the product by the shorter axis ; the quotientwill be the solidity. Examp
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