In the front row of the lowest layer there are 4 cubic inches. In both rows of the layer there are 2 times 4 cubic inches, or 8 cubic inches. In the six layers there are 6 times 8 cubic inches, or 48 cubic inches. The steps taken are: First. Determine the unit of measurement. Second. Find the number of cubic units in 1 row. Third. Multiply the number of cubic units in 1 row by the number of rows. Fourth. Multiply the number of cubic units in 1 layer by the number of layers. Think first of the unit of measurement. The volume of a solid can always be found by multiplying together its length, its width, and its height, when all are expressed in the same unit of measurement (inches, feet, yards, etc.). Find the volumes of these prisms: 14. Mr. Hubbard has in his barn an oat bin 61⁄2 feet ong, 3 feet wide, and 4 feet deep. What is its capacity in cubic feet? X 15. 15. A wood box covers on the floor a space 2 ft. x 11⁄2 ft. It stands 2 ft. 4 in. high. How many cubic feet does the box occupy? 16. At 62.5 pounds to a cubic foot, what is the weight of the water contained in a tank 4 feet by 3 feet by 2 feet? 17. A cubic foot of ice weighs 57.5 pounds. What is the weight of a cake 2 feet long, 2 feet wide, and 11⁄2 feet thick? 18. How many loads of earth were removed in digging a cellar 24 feet long, 18 feet wide, and 6 feet deep? Study these solutions: 1 The product of the dimensions (1) 24 × 18 × 6=2592 expressed in feet represents the con In problem work always select the shortest method. 23. Baseballs are put up in pasteboard cases 3 inches long, 3 inches wide, and 3 inches high. How many can be packed in a box 18 inches long, 15 inches wide, and 12 inches deep? 24. A pile of wood 8 feet long, 4 feet wide, and 4 feet high is 1 cord. How many cubic feet in a cord? 25. One eighth of a cord is a cord foot. How many cubic feet in a cord foot? 26. Learn: TABLE OF WOOD MEASURE 16 cubic feet1 cord foot (cd. ft.) 8 cord feet (128 cubic feet) = 1 cord (cd.) 27. How many cords in a pile of wood 16 feet by '4 feet by 4 feet? 28. How many cord feet in a pile of wood 4 feet by 4 feet by 4 feet? 1 29. At $1.25 per cord foot, what is a cord of maple wood worth? 30. Mr. Baldwin bought 3 cord feet of pine wood for $1.50. What was the rate per cord? 31. How many cords of spruce in a pile containing 704 cubic feet? 32. How many cords of hard wood in a pile containing 704 cord feet? Find the number of cords of wood in piles of these dimensions: 39. At $8 a cord, what is the value of a pile of wood 12 feet long, 4 feet wide, and 9 feet high? 40. How many cords of bark in a pile 16 feet long, 8 feet wide, and 10 feet high? 41. A freight car 30 feet long has on it a pile of pine wood 8 feet wide and 8 feet high. How many cords? SURFACES OF RECTANGULAR PRISMS 1. Draw on cardboard or stiff paper a diagram like figure 2. Cut it out. Crease on dotted lines and fold to make a rectangular prism like figure 1. Sew, pin, or paste the edges together. How many sides or faces has this prism? What is the area of the top and bottom faces? Of the front and back faces? Of the two side faces? Of the six faces? 2. Draw a diagram showing the faces of a 2-inch cube. 3. What is the surface area of a 5-inch cube? Of a 6-inch cube? 4. Represent by diagram the surface of a block of wood 2 inches by 2 inches by 3 inches. What is the surface area? t 5. Make a diagram showing the surface of a brick 8 inches long, 4 inches wide, and 2 inches thick. 1" 2". What is the surface area? = Scale 6. What is the surface area of a box 12 inches by 9 inches by 3 inches? Scale 1" 3". 7. Find the surface areas of the prisms in examples 2 to 13 on page 101. 8. Make a diagram of the outside surface of a rectangular collar box without cover. Of an envelope box. 1. This diagram represents a field divided into four lots. Copy it, and answer these questions about it (1) What kind of figure is lot No. 1? What are its dimensions? What is its area in acres? |