MISCELLANEOUS PROBLEMS 1. Reduce 1 ream 16 quires 20 sheets to a fraction of a bale. 3. Reduce 8 gross 9 doz. to units. 4. Reduce of a quire to a fraction of a bundle. 5. Find the gain on a carload of coal weighing 25 long tons bought at $5.25 per long ton, and sold at $6.12 per short ton. 6. Reduce of a day to hours, minutes, and seconds. 7. I bought a city lot containing 24 acres for $6500 an acre, and sold it for $.25 per square foot. Did I gain or lose, and how much? 8. I bought 12 bu. of cherries at $2.50 a bu., and sold them at 12¢ a quart. How much did I gain or lose? 9. Find the cost of 3856 laths at $3.25 per M. 10. Find the cost of 4380 pounds of hay at $16 a ton. 11. An American bought in London 12 yards of cloth at 16 shillings a yard, 2 suits of clothes at £4 and 10 shillings each, and an overcoat for £6. What was his bill in U. S. money? 12. An American lady bought in Paris 10 yards of lace at 25 francs a yard and 8 pairs of gloves at 8 francs a pair. What was her bill in U. S. money? 13. If a piece of city property 240 feet deep by 350 feet front costs $10,000 and is sold in lots of 50 feet frontage at $2000 each, what is the gain? 14. How many times will a wheel whose circumference is 15 feet revolve in going 10 miles? 15. Reduce 125 yards 2 feet 6.5 inches to a decimal fraction of a mile. 16. A haymow contains 78,600 cubic feet. How many tons of timothy hay will it hold? How many tons of clover will it hold? 17. A wagon box contains 100 cubic feet. How many tons of coal will it hold when full but not heaped? 18. Reduce 20 cubic yards 12 cubic feet to cubic inches. 19. Reduce 24,400 cubic inches to cubic yards. MISCELLANEOUS WORK 1. At 98 cents a bushel find the value of a load of corn weighing 2980 pounds. (One bushel weighs 70 pounds.) 2. An American merchant bought goods in France for 280,400 francs. What did the goods cost him in U. S. money? (1 franc = $0.193.) 3. Following is the record of 10 loads of wheat: At $1.48 a bushel, find the value of this wheat. 4. At $18.40 a ton, what is the value of a load of hay whose net weight is 3190? 5. A can do a piece of work in 7 days, B can do it in 8 days, and C in 9 days. What fraction of the work can they do in one day when all are working together? 6. In one lumber camp 540 bushels of oats are fed to 45 horses in 30 days. At this rate how many bushels should be fed to 117 horses in 115 days? Find the total in each of the following: CHAPTER XVII MENSURATION 208. Uses of Mensuration. Mensuration (indirect measurement, see § 211) is of constant use in many trades, professions, and in many kinds of business. The manifold and frequent uses of mensuration will appear throughout this chapter. It is one of the most important parts of business arithmetic. 209. There are two kinds of measurement ; namely, direct measurement and indirect measurement. 210. Direct Measurement. Direct measurement consists in applying a unit to a magnitude of the same kind to see how many times the unit is contained in it. Thus, we may measure the length of an object by applying a foot measure or a yard measure directly to the object to see how many times the unit is contained in its length. Similarly, we may measure the contents of a milk can by finding how many times a quart measure may be filled from it. 211. Indirect Measurement. Indirect measurement consists in measuring a quantity by any means other than the direct application of the unit of measure to the quantity to be measured. Thus, we measure the area of a rectangle by taking the product of its length and width. The unit of measure (the square foot or the square rod) is not applied at all to the quantity to be measured. Similarly, the volumes of bins, cisterns, and tanks are obtained indirectly by measuring the dimensions (length, width, depth) by means of a linear unit, and then computing the volume. 212. Definition of Mensuration. - Mensuration is the art of indirect measurement. 213. Measurement of Lengths. - Indirect measurement of length is, in general, more difficult than indirect measurement of area or volume. In this book, the only method given for measuring length indirectly is the one given in §§ 218, 219. 214. Area of a Rectangle. It is seen by inspection of the figure that the number of unit squares contained in a rectangle is equal to the product of its length and width. Thus, if the rectangle is five inches long and four inches wide, it contains 4×5 square inches. The general rule may be stated as follows: To use this rule, the length and the width must be measured by the same unit. If the length and width are measured in feet, the area will be given in square feet; if the length and width are measured in rods, the area will be given in square rods; etc. It is easily seen from Figure 2 that the area of the triangle ABC is half the area of the rectangle ABDE. VOLUMES 216. Volume of a Rectangular Solid. A solid figure in the shape of a box is called a rectangular solid. We can easily see from the figure that the number of cubic units of a rectangular solid equals the product of the length, width, and depth. Thus, if a box is 5 feet long, 4 feet wide, and 3 feet deep, its cubical contents are 5 X 4× 3 = 60 cubic feet. The product 5 X 4 gives the number of cubic yards in a layer 5 yards by 4 yards and one yard deep. The three dimensions of the solid must be expressed in the same unit. The volume will then be expressed in terms of a cubic unit whose edge is the unit of length used in measuring the dimensions. That is, if all the dimensions are expressed in inches, then the volume will be expressed in cubic inches. Again, if the dimensions are expressed in feet, the volume will be expressed in cubic feet, etc. PROBLEMS 1. How many acres are there in a field 60 rods wide and 110 rods long? See page 130. 2. A surveyor finds that a rectangular field is 1650 feet wide and 2395 feet long. How many acres does it contain? See page 130. Find the result accurate to two places of decimals. 3. The base of a triangle is 17 feet and its altitude on that base 14 feet. Find its area. 4. The area of a triangle is 36 square feet. If the base is 9 feet, what is the altitude? 5. If the dimensions of a rectangular solid are given in inches, how may the volume be found in cubic feet? 6. If the volume of a rectangular solid is known and also its length and width, how may its depth be found? 7. If the volume of a rectangular solid is known and also its length and depth, how may its width be found? |