Ex. I. dimensions are 14, 18, 36 inches. Find the solidity of a parallelopipedon whose I 2 I 6 Ex. 2. Find the number of gallons contained in a rectangular cistern whose dimensions are 6 ft. 3 in., 4 ft. 4 in., 5 ft. 8 in. 75 52 150 375 3900 68 31200 23400 2,7,7,2,7,4) 2652000 (955 455 galls. 2495466 156534 138637 17897 16636 1261 1109 152 14 14 XXIV. Given the breadth and thickness of a rectangular beam, to find the length when the solidity is given. Divide the solidity by the product of the length and breadth. Ex. The breadth and thickness of a beam are 20 and 15 inches; find the length of a piece which contains 10 cubic feet. 10 ÷ (1 × 13) = 10 × × 3 = 4 feet. EXAMPLES. I. 1. Find the solidity of a parallelopipedon whose dimensions are 16, 18, 30 inches. Ans. 5 c. ft. 2. Find the solidity and surface of a parallelopipedon whose dimensions are 6 ft. 3 in., 4 ft. 6 in., 3ft. 9 in. Solidity, 1051 c. ft. 3. Find the number of gallons in whose dimensions are 1, 1, 13 yards. Surface, 1367 sq. ft. a rectangular cistern Ans. 552 galls. I pt. 4. The breadth and thickness of a beam are 7 and 5 inches; find what length must be cut off to contain 1967 cubic inches. Ans. 5 inches. 5. The length and breadth of a tank are 60 and 42 feet; find the depth in order that it may contain 840 cubic yards. Ans. 9 feet. 6. The breadth and thickness of a beam are 3 ft. 3 in. and 2 ft. 4in.; find by duodecimals the length of a piece which contains 14 cubic feet. Ans. I feet. 7. Find the size of a cube whose solidity is equal to that of a parallelopipedon whose dimensions are 1 ft. 8 in., 2 ft. 8 in., 4 ft. 1 in. Ans. 2 ft. 4 in. 8. The three contiguous edges of a parallelopipedon are 8, 10, 12; find the lengths of three lines drawn from one corner to the middle points of the opposite faces. Ans. 11180, 12*324, 13.601. 9. The length and breadth of a 56 lb. weight are 8 and 6 inches; find the height, allowing 2 lbs. for the handle which is sunk into the weight. Ans. 4 inches. THE PRISM. This solid is contained by rectangular planes, all parallel to the same straight line; the ends are equal rectilineal figures. XXV. To find the solidity of a prism. Multiply the area of the end by the length. T. M. 5 Ex. Find the solidity of a pentagonal prism whose length is 7 ft. 3 in.; the side of the pentagon being 3 ft. 6 in. I. Find the solidity of a prism whose length is 20 ft. 6 in.; the end being an equilateral triangle whose side is 14 ft. 10 in. Ans. 1953 076 feet. 2. Find the solidity of a triangular prism whose length is 12 ft. 9 in.; the sides of the end being 7 ft. 3 in., 8 ft. 4 in., 9 ft. 5 in. Ans. 370 211 feet. 3. Find the solidity of an hexagonal prism whose length is 10 ft. 10 in.; the side of the hexagon being 5 ft. 5 in. Ans. 825 782 feet. 4. Find the solidity of a triangular prism whose length is 6 feet; the sides of the triangle being 2 ft. 1 in., 3 ft. 3 in., 4 ft. 8 in. Ans. 17 feet. THE CYLINDER. This solid is formed by the revolution of a rectangle about one of its sides. XXVI. To find the curve surface of a cylinder. Multiply the length by the diameter; then multiply by 3. Ex. Find the curve surface of a cylinder whose length is 10 ft. 3 in., and diameter 3 ft. 11 in. |