MEASURING LUMBER MEASURING LUMBER 303 You have learned that to measure anything is to compare it with a unit of measure. To measure lumber, the unit of measure is called a board foot, which is a board one foot square and one inch thick, or its equivalent in lumber of any shape. In measuring lumber less than 1 inch thick, the thickness is considered as if it were 1 inch thick. That is, a piece one foot square is a board foot. When sold in large quantities, the price of lumber is quoted by the thousand board feet. Thus a quotation of "$48 per M" means $48 for 1000 bd. ft. NOTE. By lumbermen the term "foot" is often used instead of "board foot." 1. Frank needed 9 boards each 12 ft. long, 8 in. wide, and 1 in. thick to build a house for his hens. How many board feet did he need? 3 ft., Since 8 in. = each linear or running 9 × 12 X bd. ft. = 72 bd. ft. foot of a board 8 in. wide and 1 in. thick is of a board foot. 2. Frank also needed 4 pieces of lumber 2 in. by 4 in. and 12 ft. long in making a yard for his hens. Find how much lumber in the four pieces. 4 A piece 2 in. by 4 4 X 12 X bd. ft. 32 bd. ft. in. is just as large as a 2 3 = piece 1 in. by 8 in. 3. For posts Frank wanted 10 pieces 4 in. by 4 in. and 6 ft. long. Find how much lumber in the ten pieces. SUGGESTION. A piece 4 in. by 4 in. contains as much lumber as a piece 1 in. by 16 in. Hence there are 1 bd. ft. to each running foot in each post. Make a drawing on the blackboard to show this. That is, draw a 4-inch square and divide it into 4 strips each 1 inch thick and lay them end to end. 4. Some boys wanted to make a small "shack" for a camp to use when going on hikes. A dealer offered to furnish rough lumber for $45 per 1000 bd. ft. Here is the lumber needed. Make out a bill for it. 2 sides each 6 ft. by 12 ft.. BOARD FEET ? ? ? ? ? 2 ends each 6 ft. by 10 ft.. ? ? 5. Some boys living on a lake built a float from which to dive. The float was 12 feet square. They used 2-inch lumber for the platform, and 4 pieces each 3 in. by 6 in. by 12 ft. for the frame. Find the cost of the lumber at $65 per M. 6. The same boys made a boat dock from lumber 2 inches thick. The dock was 3 ft. wide and 16 ft. long. They also used 2 pieces each 3 in. by 6 in. by 16 ft. Find the cost of the lumber at $48 per M. MEASURING RECTANGULAR PRISMS MEASURING RECTANGULAR PRISMS 305 A rectangular prism is a solid bounded by six faces all of which are rectangles. When the six faces are all squares, the figure is called a cube. A rectangular prism has length, breadth, and thickness. These are called its dimensions. The measure of a rectangular prism is called its volume. The unit of measure in measuring volumes is some cube whose edge is a linear unit. PRISM To measure a rectangular prism is to find how many unit cubes it will contain. Thus, the prism shown here is 3 units wide, 3 units high, and 4 units long. Suppose that these are inches. Then it is seen that in the layer 1 in. thick, shown at the right, there are 3 rows of cubes each containing 4 cu. in., and that the prism is equal to 3 such layers. Hence, the volume equals 3 X 3 X 4 cu. in. 36 cu. in. = The number of cubic units in any rectangular prism is equal to the product of the number of linear units in its three dimensions. As a formula this is expressed by V=IX w X h. 1. Find the volume of a rectangular prism 4 in. wide, 3 in. thick, and 8 in. long. Find the volumes of rectangular prisms: 9. 10 ft. by 2 ft. by 4 ft. 5. 5 ft. by 6 ft. by 10 ft. 10. A brick 2 in. thick, 4 in. wide, and 8 in. long contains how many cubic inches? 11. A bin of wheat 6 ft. wide, 10 ft. long, and filled to a depth of 4 ft. contains how many cubic feet of wheat? 1 cu. ft. is equal to .8 bu. How many bushels of wheat in the bin? 12. A box 18 in. wide, 27 in. long, and 15 in. deep will hold how many bushels? 13. There are 231 cu. in. in a gallon. Show that a box 3 in. deep, 7 in. wide, and 11 in. long will contain a gallon. 14. A can of maple sirup 5 in. by 6 in. and 8 in. high will hold how much more than a gallon? 15. A farmer has a concrete watering trough 30 in. wide, 5 ft. long, and 20 in. deep. How many gallons will it hold? 16. A cubic yard of earth is called a load. How many loads in an excavation for a cellar 20 ft. wide, 24 ft. long, and 6 ft. deep? 17. A pile of wood 4 ft. wide, 6 ft. high, and 14 ft. long contains how many cubic feet? 128 cu. ft. are called a cord. How many cords in the pile? 18. A coal bin 10 ft. by 12 ft. will hold how much coal when filled to a depth of 6 ft.? (Estimate 35 cu. ft. to the ton.) MEASURING BOXES, BINS, AND TANKS 307 19. Frank kept feed for his rabbits in two boxes: one was 10 in. by 14 in. and 8 in. deep; the other was 14 in. by 20 in. and 12 in. deep. The larger box will hold how many times as much feed as the smaller one? 20. For asparagus beds James made an excavation 6 ft. wide, 18 ft. long, and 11⁄2 ft. deep. Ralph made one 8 ft. wide, 20 ft. long, and 14 ft. deep. amount of excavating and how much? Who did the greater 21. A schoolroom should allow 200 cu. ft. of space for each pupil. Measure your schoolroom and see how many cubic feet of space there are for each pupil. MEASURING BOXES, BINS, AND TANKS In the problems that follow, use the following tables: 1. A can 12 in. square and 14 in. deep will hold how many gallons? 2. A swimming tank 20 ft. by 40 ft. will hold approximately how many gallons when filled to an average depth of 5 ft.? 3. A watering trough 10 ft. long, 32 in. wide, and 14 in. deep will hold how many gallons? 4. A box 10 in. by 12 in. and 9 in. deep will hold what part of a bushel? 5. A box 32 in. wide, 40 in. long, and 28 in. deep will hold how many bushels? 6. A bin 12 ft. by 14 ft. will hold approximately how many bushels when filled to an average depth of 6 ft.? |