73. If a shop has been paying its men for ten hours' work and then pays them the same day's wage for an eight-hour day, what per cent of increase does each man receive ? 74. Determine the length of the diagonal of a cube if the length of each edge of the cube is 12 inches. 75. On May 30, 1914, Thomas drove a Delage at Indianapolis a distance of 500 miles in 6 hours, 3 minutes, 45.94 seconds. What was his average speed in miles per hour ? In miles per minute? 76. A Bessemer converter contains 10 tons of molten iron to which it is desired to add 0.5 per cent manganese. How much ferromanganese containing 20 per cent of manganese must be added ? 77. A rectangular box is 6 feet long, 4 feet wide, and 2 feet deep. Determine the dimensions of a similarly shaped box whose length is 8 feet. 78. What is the ratio of the volume of the larger box in the preceding example to the volume of the smaller ? 79. A sugar factory consumes on an average 3000 tons of beets per day. If 75 per cent of the sugar in the beet is extracted, how many tons of sugar are produced per day from beets containing 15 per cent of sugar ? 80. If a certain grade of tool steel contains 1.2 % carbon, how many pounds of carbon are contained in 250 pounds of this steel? 81. If sheet lead 1 inch thick weighs 3.7 pounds per square foot, how many pounds will be required to line the four sides and bottom of a tank 3 feet 6 inches deep, 4 feet wide, and 8 feet long? 82. If bronze contains 85 per cenu of copper, 9 per cent of zinc, and 6 per cent of tin, what is it worth per pound when copper is worth 40 cents, zinc 7 cents, and tin 36 cents ? 83. Determine the shortest distance on the surface of a 12inch cube between two diagonally opposite corners. 84. If a soldering compound is made by fusing together 18 pounds of tin, 75 pounds of bismuth, 37.5 pounds of lead, and 19.5 pounds of cadmium, what is the percentage of each of the constituents ? 85. If the diameter of the bull's-eye on a target is the same as the diameter of a 22-caliber bullet (.22 of an inch), how great an angle of deviation in sighting is possible, if the bullet fired is to touch the bull's-eye of a target 32 feet distant ? 86. What is the value of a 30-ton carload of silver dollars if a silver dollar weighs 412 grains Troy? 87. Find the volume of a sphere whose diameter is 8 inches. 88. Determine the weight of a block of stone 9 feet 6 inches long, 2 feet 3 inches wide, and 2 feet 2 inches thick, if the weight of a cubic foot of the stone is 170 pounds. 89. A farmer delivers 5 tons of beets to a sugar factory and wants beet pulp for feed in exchange, the latter costing $ 1.60 per ton. The tare (percentage of dirt, tops, etc.) amounts to 40%, while the beets tested showed 15 % in sugar. The purity is found to be 80%. Calculate the weight of pulp received by the farmer if the company pays him 2 cents for every pound of raw sugar crystallized from his beets. 90. A, B, and C ate equally of a stock of provisions which A and B furnished. The values of what A and B contributed were in the ratio of 7 to 8 respectively. C paid $ 30 for what he ate. How should A and B have divided the money ? 91. Two gears work together. One has 36 teeth and the other 14. How many revolutions does the smaller one make while the larger one makes 28 revolutions ? 92. If cast iron weighs.26 of a pound, determine the weight of a solid spherical cast iron shot 9 inches in diameter. 93. From the answer obtained to the preceding example, determine the weight of a solid spherical cast-iron shot 41 inches in diameter. 94. Determine the diameter of a cast-iron sphere which will weigh 16 pounds. 95. The top of a mountain pass is 1500 feet higher than the level of the base and is reached by a zigzag road 6 miles long. What is the average grade of the road ? 96. A rectangular-shaped package is 1 meter long, 3 decimeters wide, and 8 centimeters thick. How many feet of string are required to tie it if the string goes around the package twice each way? 97. At the rate of 1000 yards a minute how long will it take a homing pigeon to fly 300 miles ? 98. Find the weight of 3 pine poles 2 in. by 4 in. and 14 ft. long, if pine weighs 35 pounds per cubic foot. 99. Find the area between the two circumferences if the radius of the smaller circle is 50 feet, and that of the larger is 100 feet. L 100. Find the weight of a concrete pyramid with a square base 50 feet on a side and 30 feet high, if concrete weighs 154 pounds per cubic foot. 101. What is the height of a telephone pole if the angle of elevation of the top from a point 140 feet away is 17 degrees ? 102. What is the weight of a cylindrical glass jar 12 inches tall, 9 inches in diameter, and of an inch thick? (See p. 130.) 103. What is the capacity in pints of a cylindrical can 41 inches in diameter and 43 inches high? 104. What is the weight of a pane of plate glass 40" by 30" and of an inch thick, if plate glass weighs 160 pounds per cubic foot ? 105. The following table gives the proportions of the most important substances in solution in sea water. All together they form about 3.5 per cent of the weight of the water. Chloride of Sodium .75 Chloride of Magnesium .10 Sulphate of Magnesium . .05 Sulphate of Calcium . .04 Chlorate of Potash .04 Bromide of Sodium .01 Carbonate of Calcium .005 All other substances . .005 Make a graph setting forth the above facts. 106. At 40 cents a pound for steel, find the cost of material to make 10,000 steel balls } inch in diameter for ball bearings, allowing 2 per cent for waste. 107. How many ounces of gold will be required to make one dozen gold baseball watch fobs į of an inch in diameter ? 108. If water in a 6-inch irrigating pipe is flowing at the rate of 8 feet per minute, how many gallons of water are delivered per hour at the end of the pipe? 109. How many feet of belting are there in a roll of 40 turns where the diameter of the roll is 32 inches and the diameter of the eye is 5 inches ? 110. How many gallons of oil in an upright cylindrical tank 10 feet in diameter and 10 feet high, if it is filled to a depth of 3 feet 6 inches ? 111. Determine the number of gallons of water a hemispherical bowl 16 inches in diameter will contain. 112. How many feet of pipe 2 inches outside diameter, i inch thick, can be made from 1 ton of lead, allowing 5 per cent for waste, if lead weighs 710 pounds per cubic foot ? 113. What is the cost of putting a 4-foot sidewalk along the front and one side of a lot 60 feet by 160 feet at 15 cents per square yard ? 114. Prepare a table for the conversion of French units of length into English units of length. 115. How many cones 2 inches in diameter at the top and 5 inches deep can be filled with 1 gallon of ice cream ? |