2368 .7854 9472 11840 18944 16576 18598272 6.6 = the height 111589632 6197424 12398.8480 Anf. as above. Ex. 2. What is the solidity of the frustum of a cone, its height being 50 feet, the diameter at the greater end 20, and at the less end 10 feet? Ans. 9163 folid feet. Ex. 3. Required the folid content of the frustum of a cone, the altitude being 9, the greater diameter 4, and the lesser 2. Anf. 65.9736. Ex. 4. Required the folidity of the frustum of a cone, whose height is 38 inches, the diameters being 16, and 9 inches. Anf. 4785.1804. Ex. 5. What is the solidity of a log of wood, whose bases are squares, their fides being 10 and 15 inches, and length 18 feet? Anf. 19.7916 Ex. 6. What is the folidity of the fruftum of a hexagonal pyramid, the height being 12 feet, the side of the greater end 3 feet, and the lefser 2 ? Anf. 197.453472 feet. Ex. 7. Required the content of the frustum of an octagonal pyramid, its height being 20 feet, the sides of its bases 10 and 6 feet respectively. Anf. 6309.14431 cubic feet. Ex. 8. Required the folidity of a mast, i feet diameter at the the greater base, and 1 foot at the lefser, its length being 72 feet. Anf. 89.5356 cubic feet. PROBLEM IX. To find the folidity of the prismoid. RULE I. To the areas of the two ends add four times the area of the middle section. Multiply the sum by the height, and š the product will be the solidity. Rule 2. To the longest side of the leffer base add half the longest fide of the greater base, and multiply the sum by the breadth of the lefser bafe ; reserve this product. Again : To the longest of the greater base add half the longest side of the lefser base, and multiply the sum by the breadth of the greater base; and to the product add the product formerly reserved; multiply this sum by the height, and the product will give the solidity, EXAMPLE I, Required the folidity of a quadrilateral prismoid, of which the shortest and longest sides of the greater base are 20 and 16 feet, and the corresponding sides of the lefler base 12 and 10 feet, the height being 40 feet 12 the longest side of the leffer base. 22 220 reserved number, Again, 20 the longest side of the greater base, 6 half the longest side of the lefler base. 26 416 416 636 3)25440 8480 cubic feet as above. Ex. 2. Required the solid content of a trough, in the form of a prismoid, whose greater base is 24 inches by 30, and lefler base 20 inches by 24, the depth being 18 inches. Anf 10728. Ex. 3. What is the content of the hopper of a mill, 4 feet by s at the greater base, and 12 inches by so at the lesser, its , depth being 4 feet ? Ans: 57408 folid inches, or 33.2 feet, PROBLEM X. To find the folidity of a wedge RULE. Multiply the sum of twice the length of the base, and the length of the edge by the product of the height of the wedge into the breadth of the base, and of the last product will be the folidity Nite. When the length of the base is equal to that of the edge, the wedge is equal to one half a prism of the same base and altitude, EXAMPLE I. How many solid feet are in a wedge whose base is 2 feet 8 inches long and 44 inches broad, its perpendicular height being 14 inches, and the length of the edge i foot 9 inches ? Multiply the circumference by the diameter, and the productwill be the surface : Or, Multiply the square of the diameter by 3.1416 for the sur-. face. Rule 2. Multiply the square of the axis by .7854, and four times the product will be the superficies. EXAMPLE I. How many square inches will cover a globe of 6 inches diameter? Note. 4 times the area of a great circle of a sphere is equal to its surface. Ву |