BOARD MEASUREMENT The unit of measurement of lumber is the board foot, which is the amount of lumber in a board 1 ft. long, 1 ft. wide, and 1 in. thick. A board 12' long, 1′ wide, 1′′ thick contains 12 board feet; a board 12' 1' X21" contains 30 board feet. Tell the number of board feet in boards: 1. 8' x3" and 1 in. thick. 2. 20' x6" and 1 in. thick. 3. 12'x14" and 2 in. thick. 4. 12'x12" and 11" thick. 5. 15'x16" and 2" thick. 6. 18'x18' and 24" thick. 7. How many board feet are there in a plank 18′ long, 11⁄2 wide, and 14" thick? 8. How many board feet in 10 beams 20' x6"x4"? In 17 beams? 9. Find the cost of 40 pine boards 24' 9"x1" at $18 per M. 10. Tell the cost of 75 cedar joists 12'x11"x4" at $25 per M. 11. Find the cost of 150 pieces of board, each 15' ×121" x11" at 8¢ per ft. 12. If a plank 12′×9′′×2′′ is cut into boards 1" thick, how many sq. ft. will they cover? 13. Estimate the cost of the labor in laying a hardwood floor 20'x24' at $8 per thousand square feet of surface. 14. What will be the cost of flooring a room 22'×36', with lumber 1" thick at $30 per M? 15. Find the cost of the flooring for a room 48′ ×40′ at $4.50 per thousand sq. ft., allowing of the floor area for loss in cutting and overlapping. 16. At $7.20 per 1000 sq. ft., figure the cost of matched flooring for a reception hall 75'x50'. If it takes two men 8 hours each at 60¢ an hour to lay the floor, compute the total cost. PAVING AND EXCAVATING Estimates for pavements, sidewalks, and roadbeds are based on the square yard or square foot. The cost of excavation is based on the cubic yard. 1. What will it cost, at 28¢ per sq. ft., to construct a sidewalk 6 wide and 98' long? 2. A concrete foundation for a pavement is 50' wide and 924 yd. long. How much will it cost at $.90 per sq. yd.? At $2.10 per sq. yd. what will it cost to pave with brick the following lengths of street and sidewalk: 3. 180 yd. X9' 4. 680'x12' 5. 520'x8' 6" 7. 410 yd. X3 yd. 8. 500 yd. X11′ 6′′ 9. A street 825′ long and 32′ wide can be asphalted at a cost of $2.25 per sq. yd., or paved with brick at $1.70 per sq. yd. How much cheaper will the brick pavement be? 10. To prepare it for asphalt paving, a street 830 yd. long and 48′ wide is excavated to an average depth of 15 in. How many cubic yards of earth are removed? What will this cost at 45¢ per cu. yd.? Find the cost of digging the following cellars at the price given per cu. yd.: 13. 42′ ×38′×61′ @ $.42 14. 35′×30′×8′4′′ @ $.40 11. 60'50'x9' @ $.50 12. 48′×30'×6′ @ $.42 15. How much will it cost at 20¢ per cu. yd., to remove snow from a city street 1 mi. long and 30′ wide, when the snow is 6" deep? 16. If a dirt car can carry 18 cu. yd. of earth, how many carloads will be moved in excavating a space 567' 84' and 24' deep? 17. A trench is 620' long, 18" wide, and 6' 6" deep. Find the cost of excavation at $1.25 per cu. yd. 1. A tank is 12'x4'x4'. How many gal. will it contain? Compute the contents in gal. of the following tanks: 2. 3'x4'x8' 3. 4' 5" x3' 1" ×2′ 6′′ 4. 2'6" X3'6"×10' 5. 15" x12'x10" 6. Compute the weight of the water in a tank 8'×6′ 6′′ ×5′ when the tank is full. 7. How many barrels of oil will be contained in a tank 10'x7'x9'? 8. Find the weight of 147 gallons of water. 9. A cylindrical tank is 15' high and the inside diameter of the base is 4'. How many gal. will it contain? 10. About how many cu. ft. of water are there in a tank containing 9000 gal.? 11. How many cu. in. in 23 bu.? 12. In 132 bu. how many cu. ft. are there? 13. How many bu. will be contained in a space of 900 cu. ft.? 14. A rectangular bin is 20′ ×8'x5'. How many bushels will it hold? 15. If a ton of coal occupies about 35 cu. ft., about how many tons can be stored in a bin 18'×8′ 6′′×6′? 16. How many bu. will a bin 12'x7' hold if 4' deep? 17. A wagon body is 10' 6" long, 1 yd. wide, and 30" high. How many cu. ft. will it contain? 18. A bushel of corn weighs 56 lb. Figure the weight of the corn in a bin 8'x4'x3'. 19. A box is 7′ 4′′ long, 2′ wide, and 3' 4" deep. How many cu. ft. does it contain? FORMS OF GRAPHS We can often make others grasp more readily and understand more clearly the practical significance of figures by using a diagram or a graph. A "graphic" illustration serves to visualize certain relationships otherwise difficult to comprehend. For example, however clearly one may grasp the relative values of the manufactured goods exported from the United States, when one reads that the total was $20,000,000 in 1840, $25,000,000 in 1850, $50,000,000 in 1860, etc., and $1,190,000,000 in 1913, the great increase in our manufactures seems almost vivid to us when it is represented in the form of graph as above. Here each square represents $50,000,000. WRITTEN PROBLEMS 1. Draw a diagram in which each square shall represent a production of 5 million bushels, so as to show graphically the wheat production of the following states: Oklahoma, 15 millions; Indiana, 30 millions; Kansas, 38 millions; S. Dakota, 44 millions; Ohio, 50 millions; N. Dakota, 59 millions; Minnesota, 75 millions. 2. Construct a graph to show world coal production in tons: Great Britain, 290 millions; Austria-Hungary, 55 millions; United States, 420 millions; Germany, 240 millions; Russia, 29 millions; Belgium, 24 millions. 3. Show graphically the population of the continents: North America, 110 millions; South America, 35 millions; Europe, 400 millions; Australia, 3 millions; Asia, 910 millions; Africa, 175 millions. 4. Show graphically the chief expenditures of the United States as given on page 123. 5. Show by a graph the production of plantation rubber in tons during these years; 1905, 140 tons; 1906, 510; 1907, 1000; 1908, 1800; 1908, 3600; 1910, 8200; 1911, 14,100; 1912, 28,500; 1913, 42,000. Besides being used to show relative quantities such as those given above, graphs are widely used to show the nature or degree of variations or numerical changes. They can illustrate changes in rainfall, temperature, pressure, population, transportation, etc. This graph shows the variation in the number of passengers carried by a ferry-line during each day of a two weeks' period. The successive days are represented on the horizontal lines and the number of passengers on the vertical lines; as, Monday 525 Tuesday 560, etc. |