Board Measure. 355. Boards one inch or less in thickness are sold by the square foot. Boards more than one inch in thickness, and all squared lumber, are sold by the number of square feet of boards one inch in thickness to which they are equivalent. Thus, a board 16 ft. long, 1 ft. wide, and 1 in. thick contains 16 ft. board measure. If only,, or of an inch thick, it still contains 16 ft.; but if 1 in. thick, it contains 1 × 16, or 20 ft. board measure. 356. To Find the Number of Feet Board Measure in Boards an Inch or More in Thickness, and Squared Lumber, Express the length and width in feet, and the thickness in inches; take the product of these three numbers for the number of feet board measure. NOTE 1. In practice, the width of a board, unless sawed to order, is reckoned only to the next smaller half-inch. Thus, a width of 11 in. is reckoned 11 in.; of 133 or 134 in. is reckoned 13 in. NOTE 2. If a board tapers regularly, its average width is found by taking one half the sum of its end widths. How many feet board measure in : 26. A board 18 ft. long, 9 in. wide, in. thick? 27. A board 16 ft. long, 11 in. wide, 1 in. thick? 28. Twenty boards averaging 14 ft. long, 10 in. wide, 1 in. thick? 29. Three joists 13 ft. long, 8 in. wide, 3 in. thick ? 30. A stick of timber 8 in. by 9 in., and 27 ft. long? 31. Two beams, each 6 in. by 9 in., and 23 ft. long? 32. Three joists, each 3 in. by 4 in., and 11 ft. long? 33. Five joists, each 6 in. by 4 in., and 14 ft. long? 34. A stick of timber 10 in. square, and 36 ft. long? 35. Ten planks, each 13 ft. long, 15 in. wide, 2 in. thick? Find the cost of: 36. Nine joists, each 15 ft. long, 3 in. by 5 in., at $12 per M. NOTE. The abbreviation per M means by the thousand. 37. Thirty planks, each 12 ft. long, 11 in. wide, 3 in. thick, at $15 per M. 38. Four sticks of timber, each 8 in. by 9 in. and 23 ft. long, at $18 per M. 39. A board 24 ft. long, 23 in. wide at one end and 17 in. at the other, and 11⁄2 in. thick, at $30 per M. 40. A stick of timber 29 ft. long, 10 in. by 12 in., at $13.50 per M. 41. The flooring for two floors, each 23 ft. by 17 ft., each floor double, and of boards in. thick; the under floors at $18, and the upper at $24, per M. 42. The flooring timbers for a room 23 ft. by 17 ft., at $18 per M, if they are 2 in. by 10 in., 17 ft. long, and are placed on edge, one close to each wall and the others with spaces 3 ft. wide between them. 357. Round Logs. Round logs are sold by the number of feet board measure that can be cut from them. If a log is not more than 16 ft. long, we measure the length of the log and the diameter of the smaller end, and find the number of feet board measure as follows: Subtract twice the diameter expressed in inches from the square of the diameter, and take 21 of the remainder for the number of feet board measure in a log 10 ft. long. 43. Find the number of feet board measure in a log 12 ft. long, and 20 in. in diameter at the smaller end. SOLUTION. 2022 × 20 400 40 = 360. 21 of 360 189. As the log is 12 ft. long, we must take 12 of 189 ft. to obtain the number of feet in the whole log; that is, 226.8 ft. By this rule find the number of feet board measure in : 44. A log 14 ft. long, smallest diameter 17 in. 45. A log 11 ft. long, smallest diameter 13 in. 46. A log 16 ft. long, smallest diameter 20 in. 47. A log 12 ft. long, smallest diameter 15 in. Find the value at $9 per M of: 48. A log 15 ft. long, smallest diameter 11 in. 49. A log 16 ft. long, smallest diameter 13 in. 50. A log 13 ft. long, smallest diameter 16 in. 51. A log 14 ft. long, smallest diameter 12 in. 358. Large, heavy timber of hard wood is generally sold by the ton, signifying 50 cu. ft., or 600 ft. board measure. Volumes. 359. If the length, breadth, and height of a rectangular solid are expressed in the same linear unit, the product of these three numbers will express its volume in cubic units of the same name (§ 161). Also, the number of cubic units in a rectangular solid divided by the product of the numbers of linear units in any two dimensions gives the number of linear units in the third dimension (§ 161). EXERCISE 90. 1. Find the volume of a rectangular solid 7 ft. long, 2 ft. 6 in. wide, and 11 in. thick. 2. How many cubic feet of air in a hall 54 ft. long, 33 ft. wide, and 21 ft. 4 in. high? 3. Find the volume of a cube whose edge is 2 yd. 4. A cellar was dug 21 ft. long, 17 ft. 3 in. wide, and 9 ft. deep. How many cubic yards of earth were taken out? 5. Find the volume of a brick 8 in. long, 3 in. wide, and 24 in. thick. 6. How many cubic feet of water will a rectangular cistern hold whose length, breadth, and height are 5 ft. 4 in., 3 ft. 6 in., and 2 ft. 10 in., respectively? 7. Find the volume in cubic inches of a bar of iron 21 ft. long, 3 in. wide, and 2 in. thick. 8. What is the value at $190 a cubic inch of a bar of gold 8 in. long and of an inch square? 9. A rectangular reservoir 15 yd. long, 12 yd. wide, holds 330 cu. yd. of water. What is its depth? 10. What length must be cut off a beam 9 in. by 15 in. that the part cut off may contain 2 cu. ft.? 11. How high is a room, if it is 31 ft. 3 in. long, 24 ft. broad, and contains 10,000 cu. ft. of air? 12. A piece of wood 5 ft. long, 1 ft. broad, and 9 in. thick is cut up into matches 21⁄2 in. long and 0.1 of an inch square. How many matches will there be, if no allowance is made for waste in cutting? 13. How long a wall 6 ft. high, 12 in. thick, can be built with the bricks forming a rectangular pile 17 ft. 6 in. long, 5 ft. wide, and 4 ft. 3 in. high? 14. Find the surface of a cube whose edge is 3 ft. 53 in. 15. Find the surface of a rectangular block of stone 4 ft. long, 2 ft. broad, and 14 ft. thick. 16. A lake whose area is 45 A. is covered with ice 3 in. thick. Find the weight of the ice in tons, if a cubic foot of ice weighs 920 oz. 17. How many bricks will be required to build a wall 75 ft. long, 6 ft. high, and 16 in. thick, if each brick is 8 in. long, 4 in. wide, and 24 in. thick? 18. The ceiling of a room 27 ft. long, 24 ft. broad, and 10 ft. high is to be raised so as to increase the space by 84 cu. yd. What will then be the height of the room? 19. Find the cost of making a road 110 yd. long and 18 ft. wide, if the soil is first removed to the depth of 1 ft. at a cost of 25 cents a cubic yard, rubble then laid 8 in. deep at 25 cents a cubic yard, and gravel placed on top 9 in. thick at 62 cents a cubic yard. 20. If a rectangular block of wood 5 ft. 4.8 in. long, 1 ft. 9 in. wide and thick, weighs 7.56 cwt., find in pounds its weight per cubic foot. 360. A cord of wood or stone is a pile 8 ft. long, 4 ft. wide, and 4 ft. high, making 128 cu. ft. A cord foot is a pile 1 ft. long, 4 ft. wide, and 4 ft. high, and is therefore one eighth of a cord, or 16 cu. ft. Hence, 361. To Find the Number of Cords in a Pile of Wood, Divide the product of the length, breadth, and height, expressed in feet, by 8 X 4 X 4. 21. How many cords of wood in a pile 40 ft. long, 4 ft. wide, and 5 ft. 4 in. high? 22. A pile of wood containing 67 cords is 270 ft. long and 4 ft. wide. How high is it? 23. What will be the cost of a pile of wood 25 ft. long, 4 ft. wide, and 4 ft. 8 in. high, at $3.75 a cord? |