£305 2 s. 2 d.; May, £346 7 s. 8d.; June, £400 15s. 3 d. What did his sales average per month? 5. A package weighing 5 lb. 7 oz. 7 dr. 2 sc. 3 gr. is composed of smaller packages, each weighing 3 oz. 7 dr. 2 sc. 19 gr. How many small packages are there? SUGGESTION. Reduce to grains. 6. The driving wheels of a locomotive are each 5 yd. 2 8. Sound travels 1142 feet per second; what is the dis- MEASUREMENT OF RECTANGLES AND RECTANGULAR SOLIDS. For definitions and principles consult Chapter XV. 327. A plane surface bounded by four straight lines, and having four square corners, is a rectangle. A visiting card, a sheet of writing paper, the surfaces of a brick, are familiar examples of rectangles. 328. When the four sides of a rectangle are equal, the rectan gle is a square. 329. Take 12 pieces of stiff paper, each piece an inch square. Arrange them in 3 rows of 4 pieces each, as repre sented, making a rectangle. The number of square inches in this rectangle is the product of its two This statement is true, if the squares be arranged in other ways; as in 2 rows of 6 squares each; or 6 rows of 2 squares each. It is a general truth that 330. The area of a rectangle equals the product of its two di mensions. ORAL. 1. How many square feet in the surface of a blackboard 12 feet long, 4 feet high? 2. How many square inches in the page of a book 5 in. 3. The ceiling of a room is 12 feet square; what is its 4. How many square inches on one side of a board 12 5. How many square yards in a lot 15 by 40 yards? How many square feet? 6. How many square feet in a floor 20 feet long and 18 feet wide? How many square yards? 7. How many square feet in one side of a wall 120 feet long and 9 feet high? How many square yards? 8. How many square feet in the four walls of a room 20 feet long, 12 feet wide, and 10 feet high? SUGGESTIONS. To represent the walls of a room, take a piece of stiff paper, or thin pasteboard, 16 inches long and 2 inches wide. Each foot of the wall will be represented by of an inch of the paper or board. Fold the paper at right angles at the dotted lines. This will bring the edges A B and C D together, and the four walls of the room will be represented by the folded paper. The line A C (or B D) is the perimeter (measure around) of the room and the area of the four walls is the product of the two dimensions A C and A B. 9. How many square feet in the four walls of a room 12 feet long, 10 feet wide, and 8 feet high? 10. How many square feet in the four walls of a room 15 feet long, 12 feet wide, 10 feet high? How many square yards? How many square feet in the floor of the room? 11. How many feet long is a surface which contains 600 square feet, and is 3 feet wide? 12. How many sq. in. in a surface 9 in. long by 8 inches wide? What part of a sq. ft. is this surface? What part of a linear foot is its length? Its width? 13. What part of a square foot is a surface of a foot long by of a foot wide? ft. by ft.? ft. by 3 ft.? 10 331. A solid bounded by six rectangles is a rectangular solid. A common brick is a rectangular solid. 332. The rectangles which bound a rectangular solid are called its faces. The opposite faces of a rectangular solid are equal. Any two opposite faces may be called the upper and lower bases of the solid. The lines in which two faces meet is called an edge. 333. A rectangular solid whose six faces are equal squares is a cube. How many edges has a cube? Are they equal? Why? 334. The entire surface of a rectangular solid is the sum of the areas of its faces. The lateral surface of a rectangular solid is the sum of four of its faces, its two bases being excluded. 1. An edge of a cube is 2 inches; how many square inches in one of its faces? How many square inches on its six faces? What, then, is the entire surface of a cube whose edge is 2 inches? 2. What is the entire surface of a cube whose edge is 3 inches? 3. What is the entire surface of a cube whose edge is 10 inches? 4. What is the entire surface of a cube whose edge is 20 inches? 5. What is the lateral surface of a brick, 8 in. by 4 in. by 2 in., when its largest faces are considered its bases? SUGGESTIONS. Find the perimeter of the brick, (2×8 in. )+( 2×4 in.)= 24 in.; multiply this perimeter by the height, or thickness, of the brick, which is 2 inches. Compare this example with example 8, Art. 330, and observe that the process is the same in both. In exam. ple 8, the room is really considered as a rectangular solid, whose interior dimensions are measured. In this example, the exterior dimensions of the rectangular solid are measured. 6. Common brick are made in a wooden mold, or box, without top or bottom. What are the interior dimensions of the mold for a brick 8 in. by 4 in. by 2 in.? How many square inches in the interior lateral surface of such a mold ? 7. What is the lateral surface of a block of marble 6 ft. long, 4 ft. wide, 3 ft. high, when its smallest faces are considered its bases? What is its entire surface? 8. What is the difference in the processes of finding the entire surface of a rectangular solid, and the area of the walls, ceiling and floor of a rectangular room? 9. How many square inches on the sides and ends of a box 10 inches long, 8 inches wide, and 4 inches high? How many square inches on the top and bottom of the box? How many square inches on the entire surface? 10. A glass paper weight is 4 in. by 2 in. by 11⁄2 in. What is its entire surface? 11. A polished block of granite, 4 ft. by 3 ft. by 2 ft. was shipped in a heavy plank box. What was the interior surface of the box in sq. ft.? 12. The granite pedestal of a certain monument is 10 ft. long, 5 ft. wide, 6 ft. high, the four sides being polished. What is the area of the polished surfaces? 13. A block of writing paper is 8 in. by 4 in. by in. What is its entire surface? 14. A bureau drawer measures, inside, 3 ft. by 2 ft. by 8 in. (ft.) What is its interior surface? WRITTEN. 15. How many square feet in the floor of a hall 126 ft. long, 87 feet wide? How many square yards? 16. How many square rods in a field 320 rods long, 80 rods wide? How many acres? 17. The base of the great pyramid of Egypt is a square, 746 feet on each side. How many acres does the pyramid cover? / 18. The capitol at Washington is 751 feet long and 348 feet wide. How many acres does it cover? 19. How many square feet in 60 boards, each 16 feet long and 1 foot and 3 inches wide? SUGGESTION. Consider 3 inches as of a foot. 20. How many square feet in 40 boards, each 20 feet long and 1 foot 9 inches wide? 21. How many acres in a street 4 rods wide and 1 mile long? 22. A surveyor divided a quarter section of land into fields each 20 chains long and 10 chains wide. How many fields did he make? |