218. MEASURES OF VOLUME. 1. A Solid is a figure having length, breadth, and thick ness. 2. A Rectangular Solid is a solid bounded by six rectangles. 3. The rectangles are called the faces of the solid. 4. The intersections of the faces are called the edges. 5. Name five rectangular solids. Bring a rectangular solid to the class. Show the faces and the edges. 6. A cube is a rectangular solid whose faces are squares. 7. A cubic inch is a cube whose edges are each one inch. 8. Solids are measured by finding how many units of volume they contain. 9. The units of volume are usually cubes whose edges are linear units. 10. Complete this table: Table of Cubic Measure. cubic inches = 1 cubic foot. 128 cubic feet 100 cubic feet 11. Wood that is to be used for fuel is measured by the cord. The sticks are usually cut 4 feet long, and are then called cord-wood." For convenience in measuring they are usually "corded," that is, piled 4 feet high, the length of the stick making the width of the pile. In such a pile, for every 8 feet of length there is a cord of wood. Prove that it contains 128 cubic feet. A pile 4 feet wide, 4 feet high, and 1 foot long contains 1 cord foot. How many cubic feet does it contain? 1. Reduce 4 cubic yards 15 cubic feet 964 cubic inches to cubic inches. 2. Reduce 8 cords 7 cord feet to cubic feet. 3. Reduce 864,952 cubic inches to a compound number. 4. Reduce 1,264 cubic feet to cords, etc. 5. Reduce of a cubic yard to cubic feet and cubic inches. 6. Reduce of a cord to integers of lower denominations. 7. Reduce .36 of a cord. 8. 27 cubic inches is what part of a cubic yard? 1. How many cords of cord-wood in 3 piles of wood, each being 4 feet high, the first being 36 feet long, the second 42 feet long, and the third 73 feet long? Find its cost at $4.75 per cord. NOTE. Where cord-wood is piled 4 feet high, there is one cord for every 8 feet of length. 2. Each of the following piles is 4 feet high. Find how many cords each contains. (a) 83 feet long. (b) 69 feet long. (c) 35 feet long. (d) 47 feet long. (e) 61 feet 5 inches long. (ƒ) 93 feet 10 inches long. Find the cost of each pile at $5.25 a cord. 3. How much cord-wood in each of the following piles? What is the cost at $4.75 a cord? (a) 26 feet long, 6 feet high. Explanation. The number of cubic feet in this pile is 26 × 6 × 4. Since there are 128 cubic feet in a cord, the 26 × 6 × 4 number of cords is 128 Since cord-wood is 4 feet long, the four may be omitted from dividend and divisor, thus leaving 32 as a divisor. Note that we then divide the area of the side of the pile of 4-foot wood by the area of the side of a cord. (b) 54 feet long, 7 feet high. (c) 61 feet long, 7 feet high. (d) 42 feet 8 inches long, 6 feet 4 inches high. NOTE. Call inches twelfths of a foot, and change mixed numbers to improper fractions, thus: = 42 ft. 8 in. 423 ft. 128. 6 ft. 4 in. = 6} = 4. 128 X 19 X $4.75 3 X 3 X 32 (e) 86 feet 3 inches long, 7 feet 6 inches high. 1. The unit of lumber measure is the board foot, one foot long, one foot wide, one inch thick. 2. Lumber that is less than one inch thick is counted as if an inch thick. If lumber is more than inch thick, the excess is taken into account. 3. How many cubic inches in a board foot? How many board feet in a cubic foot? 4. What is the width of an inch board that contains as many board feet as it is feet long? 5. Of a two-inch plank? of a three-inch stud? 6. What is the end-area of each of the above pieces? 7. What is the end-area of a 6" x 8" sill? How many board feet in each foot of its length? What divisor have you employed? 8. How many board feet in a beam 10" × 12", 24 feet long? 9. Show the truth of the following: Number of board feet = thickness width x length 12 In what units must thickness, width, and length be expressed? Bills of lumber are regularly made out in these units. 222. PROBLEMS. 1. What is the cost of 16 sills 6" x 8" x 18' @ $18 per thousand feet? FORM. 16 × 6 × 8 × 18 x $18 12 × 1000 ANALYSIS. (1) Since a number of dollars is required, I write $18, the cost of 1000 board feet. I express the cost of one board foot by writing 1000 as a divisor. I express the cost of a stick 1 foot long, 1 inch wide, and 1 inch thick by writing 12 as a divisor. I multiply by 18 because the sill is 18 feet long; by 8 because it is 8 inches wide; by 6 because it is 6 inches thick; by 16 because there are 16 sills. 6 X 8 X 18 (2) The number of board feet in each sill is expressed by 12 I write 16 as a multiplier because there are 16 sills, 1000 as a divisor to get number of thousand feet, then multiply by 18 because the number of dollars paid must be 18 times the number of thousand feet. 2. What is the cost of the following bill of lumber at $21 a thousand (M)? 8 sills, 8 × 10, 16 feet long; 48 studs, 2 × 4, 18 feet long; 22 joists, 2 x 10, 16 feet long; 50 rafters, 2 × 4, 14 feet long; 24 joists, 2 x 8, 16 feet long. 3. Find the cost of the following bill of lumber, at $16.50 per M: 32 common boards, 8 inches wide, 14 feet long; 7 sills, 6 x 8, 14 feet long; 46 rafters, 2 × 6, 16 feet long; 36 joists, 2 x 8, 18 feet long. 4. Find the cost of the following bill of lumber : 5. What is the cost of 46 planks, 2 inches thick, 10 inches wide, and 18 feet long, at $22 per M.? 6. What is the cost of 65 24-inch oak planks, -12 inches wide and 16 feet long, at $36 per M.? 7. How many posts set 8 feet apart are required for wire fencing around a field 800 feet square and for two cross fences dividing the field into four equal squares? Show that the cost of these posts at 83 cents each is $49.75. |