44. If 1000 shingles are needed to cover 100 sq. ft. of roof, how many shingles are required to cover a roof 40 ft. long and 25 ft. wide, at the same rate? 45. A lawn tennis court 78 ft. long and 36 ft. wide is to be surrounded by a strip of sod 15 ft. wide at each end and 8 ft. wide at each side. What will the sodding cost at $.35 per square yard? 46. Find the cost of a half section of land at $45 per acre? 47. How many square rods are there in a rectangular field 24 ch. 45 li. long by 16 ch. 34 li. wide? 48. How many cubic inches are there in a tank containing 120 gal.? How many cubic feet? 49. How many cubic feet are there in a block of stone 5 ft. x 4 ft. 6 inches? 50. How much must I pay for a board 16 ft. long and 8 in. wide, the board being 1 in. thick and lumber costing $35 per thousand? (A board foot means 144 sq. in. of surface, not over 1 in. thick.) 51. I bought 3 boards 12' long, 6′′ wide; 8 boards 16' long, and 9" wide, and 2 boards 10' long, 12" wide. All were 2" thick. What did the whole cost at $30 per thousand? 52. What is the value of a straight pile of wood 16 ft. long, 8 ft. wide, and 6 ft. high, at $7.50 per cord? 53. What is the weight of a pile of oak boards 14 ft. long, 8 ft. 4 in. wide, and 5 ft. high, at an average weight of 54 lb. per cubic foot? 54. At $.75 a load of 1 cu. yd. what will be the cost of removing a pile of earth 60 ft. long, 24 li. wide, and 1 yd. high? 55. In one year the quarries of Minnesota yielded 4,000,000 cu. ft. of sandstone. What was this worth, at $.76 a perch? 56. Find the cost of building a stone wall 150' x 10' × 21, at $3.50 a perch. 57. A bin 12' x 8'6′′ × 5′ is filled with wheat. What is the weight of the wheat at 60 lb. per bushel? 58. What is the value of a straight pile of pine slabs 32' X 7' x 4', at $3.25 per cord? 59. A grocer paid $4.50 for a barrel of vinegar (31 gal.), and sold it at 5¢ per quart. What was his profit? 60. A jug contained 214 cu. in. of molasses. How much did it lack of containing 1 gallons? 61. What will 1 mi. of right of way for a railroad cost at $60 per acre, the width of the right of way being 100 feet? 62. What will be the cost per mile for railroad ties at $.45 apiece, the ties being laid one every 2 feet? 63. Find the cost of the rails for 1 mi. (single track) of the road, the rails weighing 77 lb. per linear yard and costing $35 per long ton. 64. Find the cost of fencing 1 mi. on both sides of the track, placing posts costing $.25 apiece 16 ft. from center to center, and using wire weighing 1080 lb. per mile at 4¢, and 30 lb. of staples @ 4¢. The fence is to be 4 wires high, and labor costs 21¢ per rod of fence. (Count the odd post.) 65. Reduce .865 gal. to smaller units. 66. Reduce .168 gal. to smaller units. 67. If oil is $.11 per gallon, what will be the cost of three 42-gallon barrels of kerosene? 68. If a certain spring regularly yields 25 gal. daily, how many barrels of the capacity of 31 gal. would it fill in 20 days? 69. A merchant bought 16 gal. 3 qt. of syrup at 38¢ a qt., and sold 27 qt. for $12; 18 qt. for $9, and the remainder at 35¢ per quart. Did he gain or lose, and how much? 70. Reduce 2 pk. 7 qt. 1 pt. to the decimal of a bushel. SOLUTION: 1 pt. = .5 qt. 7.5 qt. = 2.9375 bu .734375 bushels. 7.5 8 pk. = .9375 pk. 71. Reduce 3 pk. 5 qt. 1 pt. to bushels. 72. How many bushels will a bin hold that is 14 ft. long, 7 ft. 6 in. wide, and 5 ft. 8 in. high? 73. A farmer sold 6 loads of corn, each load averaging 36 bu. 2 pk. at 35 cents per bushel. What did he receive for the whole? 74. A boy had a bushel of hickory nuts, and sold 3 pk. 7 qt. 1 pt. What fraction of a bushel had he left? 75. If 9 bu. of potatoes cost $4.80, what is the average cost per peck? 76. A bin contained 5376.25 cu. in. of rye. How much did it lack of containing 3 bushels? 77. How many oz. of quinine will be required to prepare 12 gross of 3-grain capsules? 78. A coal dealer buys two car-loads of coal each weighing 67,200 lb., at $4.50 a long ton, and sells it at $5.75 a short ton. What is his gain? 79. How many acres of land are there in a road 4 rods wide extending around a tract of land 80 chains square? 80. How many bushels do 2240 lb. of buckwheat make in Kentucky? In California? (See table p. 102.) THE METRIC SYSTEM $76. Historical. The metric system is a decimal system of weights and measures adopted by the French Government soon after the French Revolution of 1789. The aim of the system is to base all measures upon an invariable standard, and to secure the simplest possible relations between the different units of the system. The units of length, which is fundamental to the whole system, is called the meter. It was attempted to make the meter 1 tenmillionth of the length of the part of a meridian of the earth, which reaches from the equator to the pole, called a quadrant of the earth's meridian. The meridian of the earth was measured, and 10000000 of the quadrant was obtained. A platinum bar equal to this length was very accurately cut and stored in the Government archives as the official standard of reference. Later measurements of the earth's meridian showed the former length of the meridian to be incorrect. The length of the meter as obtained from the erroneous measures was, however, retained, and the length of this bar is the standard meter. From it all the other units of the system are derived. The metric system is used for all purposes in France, and for most scientific purposes in Germany, England, and the United States. It is legalized in nearly all civilized countries. The length of the meter is 39.37 in., or about 1.1 yards. §77. Tables of Metric Measures. Fig. 1 shows a scale graduated along the upper edge to 16ths of an inch, and along the lower edge to 1000ths of a meter, called millimeters. Decimal parts of the standard units are denoted by the Latin prefixes, abbreviated in each case to a single, small letter: milli, meaning 1000th written m. Multiples of the standard units are denoted by the Greek prefixes, abbreviated in each case to a single, capital letter: deka, meaning 10 times written D. TABLE OF SURFACE MEASURE 100 sq. millimeters (mm2.) 100 sq. centimeters 100 sq. decimeters 100 sq. meters 100 sq. dekameters SQ.INCH SQ. = = = = = 1 sq. centimeter (cm2.) 1 sq. dekameter (Dm2.) 1 sq. hektometer (Hm2.) 1 sq. kilometer (Km2.) CENTI METER FIGURE 1 TABLE OF MEASURES OF Volume The standard unit of volume is the cubic meter = 35.314 |