ORAL EXERCISE 1. If C1 cu. in., what is the volume of B? of A? 245. Volume of solid. The volume of a rectangular solid equals the product of its three dimensions. This means a solid whose faces are rectangles. We do not say 4 in. times 3 in. times 2 in., but 4 times 3 times 2 cu. in. It is customary, however, to write 4 in. x 3 in. x 2 in., or 4" x 3" x 2", reading it "4 inches by 3 inches by 2 inches." WRITTEN EXERCISE 1. How many cubic inches in an aquarium 16 in. long, 8 in. wide, and 9 in. deep? 2. How many cubic feet of masonry in a wall 40 ft. long, 30 ft. high, and 1 ft. thick? 3. A cellar 24 ft. by 39 ft. by 6 ft. is to be excavated. How much will it cost at 40 ct. a load (cubic yard)? 4. The dimensions of a room are 14 ft., 12 ft., 9 ft. How many square feet of floor? of walls? of ceiling? WRITTEN EXERCISE 246. Measures occasionally used. In the following problems you may refer to these measurements: 2150.42 cu. in. 35 cu. ft. = = nearly 14 cu. ft. 1 bushel. the volume of 1 ton of coal, nearly. 500 cu. ft. the volume of 1 ton of hay, nearly. 22 bricks, including the mortar 1 cu. ft., nearly. All measures refer to inside dimensions, in examples like the following. 1 ton of hay varies from about 450 cu. ft. to 550 cu. ft., depending on the quality and how much it has settled. 1. How many bushels in a bin 7 ft. by 6 ft. by 4 ft.? (Use 14 cu. ft. 1 bu. in all such cases.) = 2. How many bushels in a bin 9 ft. by 5 ft. by 3 ft.? 3. How many bushels in a box 18 in. wide, 3 ft. long, and 2 ft. deep? 4. How many gallons in a tank 6 ft. by 5 ft. by 4 ft.? 5. How many gallons in an aquarium 14 in. long, 9 in. wide, and 11 in. deep? 6. How many gallons in a tank 61 ft. long, 31 ft. wide, and 2 ft. deep? 7. A cistern is 6 ft. square at the bottom and 5 ft. deep. How many barrels will it hold? (Use 44 cu. ft. = 1 bbl. in all such cases.) 8. An iron tank is 8 ft. long, 63 ft. wide, and 43 ft. deep. How many barrels does it contain? 9. A rectangular watering trough is 6 ft. long, 18 in. 10. A coal bin is 22 ft. long, 13 ft. wide, and 8 ft. deep. About how many tons of coal will it hold? 11. A coal bin is 16 ft. long, 81 ft. wide, and 61 ft. deep. About how many tons of coal will it hold? 12. A haymow is 22 ft. long, 14 ft. wide, and 9 ft. high. About how many tons of hay will it hold? 13. A barn has two haymows, each 24 ft. long, 15 ft. 6 in. wide, and 10 ft. high. About how many tons of hay will both hold? 14. How many cords of wood in a pile 4 ft. wide, 7 ft. high, 32 ft. long? 15. How many cords of wood in a pile 4 ft. wide, 6 ft. high, 44 ft. long? 16. If a schoolroom is 30 ft. long, 15 ft. wide, and 12 ft. high, and 180 cu. ft. should be allowed to each person, how many will the room accommodate ? 17. A tank holds 82,500 gal. feet does it contain? About how many cubic 18. An aquarium contains 3 cu. ft. About how many gallons does it hold? 19. An aquarium is 18 in. long, 91 in. wide, and 10 in. deep. How many gallons does it hold? 20. A can containing 1732.5 cu. in. is full of milk. What is the milk worth at 6 ct. a quart? 21. A wall is 321 ft. long, 2 ft. thick, and 321 ft. high. How many perches of masonry does it contain? 22. A brick wall is to be built 42 ft. long, 1 ft. thick, and 6 ft. high. About how many bricks will be needed? 64 23. How much will a mason charge for laying a wall 20 ft. long, 1 ft. thick, and 5 ft. high, at $1.87 a perch? CHAPTER II I. PERCENTAGE AND ITS APPLICATIONS. SIMPLE INTEREST. MEASUREMENTS THE FORMAL SOLUTION OF PROBLEMS 247. Solving problems. We have already (page 115) learned something about stating the solutions of problems. We are now ready to consider this part of arithmetic more fully. There are three matters which are especially important. 1. Work rapidly and accurately. The business man demands this first of all. Rapidity not only means money in the time saved, but it usually means accuracy, for when a man works rapidly he keeps his mind on his work. To insure accuracy, always check your work. One of the best checks is that of estimating the answer in advance. If the answer is not about what was expected, there is probably a mistake. This has been explained on page 88. 2. Work as the business man does. He does not put his work in steps, with signs like and +. He works in columns because it is quicker and he can more easily check his work. He also makes his work look neat, because he finds slovenly work leads to inaccuracy. 3. Analyze the problems. This means that we are to state the reasons. The business man does not write out his analyses, but he thinks them. We are asked to give analyses both orally and in writing, so we will learn to think accurately as the business man does. ORAL EXERCISE 1. If C=1 cu. in., what is the volume of B? of A? 245. Volume of solid. The volume of a rectangular solid equals the product of its three dimensions. This means a solid whose faces are rectangles. We do not say 4 in. times 3 in. times 2 in., but 4 times 3 times 2 cu. in. It is customary, however, to write 4 in. x 3 in. x 2 in., or 4" x 3" x 2", reading it "4 inches by 3 inches by 2 inches." WRITTEN EXERCISE 1. How many cubic inches in an aquarium 16 in. long, 8 in. wide, and 9 in. deep? 2. How many cubic feet of masonry in a wall 40 ft. long, 30 ft. high, and 1 ft. thick? 3. A cellar 24 ft. by 39 ft. by 6 ft. is to be excavated. How much will it cost at 40 ct. a load (cubic yard)? 4. The dimensions of a room are 14 ft., 12 ft., 9 ft. How many square feet of floor? of walls? of ceiling? |