1. How many dimensions has the cube ? Name them. 2. What dimensions has a line ? What dimensions has a surface ? a solid ? 3. Name the different units of measure in which the length of a line may be expressed. 4. Name the Ift. different units of square measure in which surface may be expressed. Ift. 5. What cubic unit have we in the first cube? Ift. 6. If a cube is 1 foot on an edge, what is the cubic unit ? 7. Draw a square 1 foot on a side. Show that it contains 144 square inches. ure. 8. Observe that 144 cubes 1 inch on an edge can be placed on a surface 1 foot square. How many layers of such cubes will it take to make a cube 1 foot on an edge ? 9. How many cubic inches equal 1 cubic foot ? 10. How many surfaces has a cube? 11. Show that all the surfaces of an inch cube are the same in area; of a 2-inch cube; of a 9-inch cube. 12. Examine carefully the figObserve: 3in. . (1) That the surface of the face upon which it rests contains 9 square inches. (2) That the first layer of units of volume contains 9 cubic inches. (3) That the whole solid, if 6 inches high, contains 6 x 9 cubic inches, or 54 cubic inches. 13. How many 1-inch cubes are there in the first layer ? how many in the solid ? 14. What is the shape of the surfaces of the solid ? Is each surface a rectangle? A rectangular solid is a solid whose surfaces are all rectangles. 15. Observe that the number of inch cubes in the solid is equal to the product of its three dimensions. 16. What is the unit of measure in the solid ? Observe that 3 x 3 x 6 x 1 cu. in. = 54 cu. in. The contents of a rectangular solid equals the unit of measure multiplied by the product of its three dimensions. TO THE TEACHER. Secure 144 1-inch cubes. 17. Build a cube 2 inches on an edge. 20. Give the different units of measure of surface; of length; of contents. 21. Find the contents of a box 3 ft. long, 2 ft. wide, and 11 ft. high. 22. Observe the cube. What is its length ? width ? height ? 23. How many 1-foot cubes 3ft. does it contain ? A cube 3 ft. on an edge is called a cubic yard. 24. Memorize this table : 3ft. 1728 cubic inches (cu. in.) 1 cubic foot (cu. ft.) = 1 cubic yard (cu. yd.) A cart load of earth is considered 1 cubic yard. PRACTICAL APPLICATIONS Excavations are estimated by the cubic yard. 1. Find the cost, at 30$ per cubic yard, of excavating a cellar 36 ft. in length, 24 ft. in width, and 4 ft. in depth. 36 x 24 x 4 x 1 cu. ft. = 3456 cu. ft., the contents of the cellar. This diagram shows the outline of a cellar 5 ft. deep. Its dimensions are given in feet. 5. How much will it 12 cost to cement the floor at $.90 per square yard ? 30 6. If a boy inhales 24 cubic inches of air at a breath, how many times must he breathe to inhale 1 cubic foot? 7. 29 pupils and their teacher occupy a schoolroom 30 ft. in length, 24 ft. in width, and 12 ft. in height. What is the average number of cubic feet of air for each person ? 8. A city lot of 371 ft. by 120 ft. is to have a layer of earth 1 ft. thick over its surface. Find the number of loads needed and its cost at 25° per load. 9. A dining room is 13 ft. by 18 ft. and has a rug on it 9 ft. by 15 ft. Find the surface not covered by the rug. 10. If the rainfall on a certain day was 24 inches, find the number of cubic inches that fell on a lot 25 feet wide and 100 feet long. Find the number of gallons. 11. Find the cost of digging a ditch, 60 rods long, 31 feet wide, and 6 feet deep, at 60 ¢ per cubic yard. 15 HAM. INT. ARITH, 12. Memorize : A gallon 231 cu. in. If a 13. Compare a 3-inch cube with a 4-inch cube. 2-inch cube weighs 6 ounces, how much will a 4-inch cube of the same material weigh ? 14. A bin is 8 ft. long, 6 ft. wide, and 4 ft. deep. Estimate quickly about the number of bushels of wheat or oats it will hold. 15. A farmer has a tank 12 ft. long, 8 ft. wide, and 6 ft. deep. How many gallons of water will it hold ? 16. How much larger is a farm 80 rods square than a farm 60 rods square ? Draw diagrams on a suitable scale to represent this. 17. The base of a rectangular tank is 48 sq. ft. and the volume is 192 cu. ft. Find the height. 18. What is the area of each surface of a cube 8 ft. on an edge ? the entire surface ? MEASUREMENT OF LUMBER Ift. Ift. A board 1 foot Ift. square and 1 inch thick or less is a board foot. 4ft. A board foot is the unit in measuring lumber. 1. Draw on the blackboard a figure to represent a board 4 feet long, 1 foot wide, and 1 inch thick. Ift. lin. |