13. Compare a 3-inch cube with a 4-inch cube. If a 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? 1. Draw on the blackboard a figure to represent a board 4 feet long, 1 foot wide, and 1 inch thick. 2. Show that this board contains 4 board feet. 3. How many board feet are there in a sill 4 ft. long, 1 ft. wide, and 4 in. thick? (2) That each board contains 4 board feet. Hence, the sill contains 4 x 4 x 1 board foot = 16 board feet. 4 in. The number of board feet in a piece of lumber equals the number of board feet in one surface multiplied by the number of inches in thickness. Find the number of board feet in the following: 4. A plank 12 ft. long, 12 in. wide, and 2 in. thick. Buying and selling lumber. Lumber is usually sold at so much per 1000 (M.) board feet. Find the cost of: 1. 5000 ft. poplar at $40 per M. 2. 500 ft. hemlock at $24 per M. 3. 10,850 ft. Georgia pine at $ 24 per M. 4. 8000 ft. white pine at $50 per M. Small bills of lumber are usually estimated at so much per board foot. = 5. Show that lumber at $40 per M. $.04 per board foot; at $27 per M. = $.027 per board foot. 6. Make out a receipted bill to Henry James for the following: 365 ft. hemlock at $25 per M., 780 ft. white pine at $40 per M., 980 ft. yellow pine at $29 per M. The dimensions 10 ft. by 6 in. by 10 in. are commonly written 10' x 6" x 10": Estimate the cost of the following at $28 per M.: 15. Observe the dimensions of the school building. What is the height of the sides of the building? 16. Find the number of board feet of siding needed for the sides and the two ends of the same height as the sides, making no allowance for openings. 17. The triangular parts at the top of the house, in Each gable can be front and in back, are called gables. divided by a line through the center of its base into two right triangles. How many board feet of siding are necessary for the two gables? 18. Find the cost of painting the siding at 10 cents per square yard. A pile of wood, of 4-foot sticks, 8 ft. in length and 4 ft. in height, is called a cord of wood. 4 x 4 x 8 x 1 cu. ft. = 128 cu. ft. = 1 cord of wood. 1. How many cords are there in a pile of 4-foot wood, 160 feet long and 4 feet high? 2. Two men cut several piles of 4-foot wood that measure in all 640 feet in length and 4 feet in height. How many cords do they cut and how much do they receive for the work at $5.50 per cord? Wood is frequently cut for house purposes into short lengths from 16 inches to 2 feet. The price of such a cord varies according to the length of the sticks. The number of cords of short wood in a pile is found by dividing the number of square feet in one side by 32. 3. At a school building there is a pile of 16-inch wood 80 ft. long and 4 ft. high. Find its cost at $1.50 per cord. 4. Two men cut 4 cords of 2-foot wood each day for 16 days. Find the cost of the cutting at 70 cents per cord. 5. One side of a pile of 2-foot wood contains 400 square feet. Find the number of cords it contains, REVIEW OF PRACTICAL MEASUREMENTS 1. How many tiles 12 in. square will be required to lay a floor 36 ft. by 15 ft.? 2. What is the length of a board walk that is 4 ft. 8 in. wide and contains 1350 sq. ft. ? 3. How many cubic yards of earth must be removed in digging a cellar 36 ft. long, 26 ft. wide, and 8 ft. deep? 4. Find the cost of covering the floor of a hall 45 ft. long and 30 ft. wide with matting, a yard wide, at 70 cents a yard. 5. How many times will the wheel of an engine 9 ft. in circumference turn in going 3000 miles? 6. Find the cost of 30 boards 16 ft. long, 12 in. wide, and 1 in. thick, at 5¢ a board foot. 7. At $.80 a bushel what is the value of a bin of wheat 16 ft. long, 8 ft. wide, and 4 ft. deep? 8. What is the number of gallons in a tank 12 ft. long, 10 ft. wide, and 8 ft. deep? 9. How much will it cost to cement the floor of a cellar 50 ft. long and 28 ft. wide at $1.08 a square yard? 10. At 7 a square yard, how much will it cost to paint the four sides of a building 50 ft. long, 20 ft. wide, and 15 ft. high? 11. My farm is in the form of a rectangle, and contains 40 What is its width, if its length is 128 rods? acres. 12. What will be the cost of plastering the ceiling of a room 22 ft. by 18 ft. at 11 a square yard? 13. A rectangular field contains 5 acres. If its length is 80 rods, what is its width? |