the number of strips will give the required number of meters, without allowance for waste in matching patterns. 23. How many meters of carpet 60cm wide will be required for a room 6m long and 5.4m wide, the strips running lengthwise? how many meters would be required if the carpet were 80cm wide? Since the room is 540cm wide, it will take 540, or 9 widths of carpet 60cm wide; that is, the amount required will be 9 × 6m 54m. If the carpet were 80cm wide, it would take 540, or 7 widths; that is, the amount required will be 7x 6m 42m. 80 = 24. How many meters of carpet 56cm wide will be required for a room 8.32m long and 6.6" wide, strips running lengthwise? 25. How many meters of carpet 70cm wide will be required for a room 7 long and 5.4" wide, strips running across the room? 26. How many meters of carpet 80cm wide will be required for a room 6m long and 5.47m wide, strips running across the room? 27. How many meters of carpet 90cm wide will be required for a room 5m long and 4.5m wide, strips running length wise? How much will it cost, at $1.875 a meter? 28. How many meters of carpet 75cm wide will be required for a room 5.25m long and 4.75m wide, strips running across the room? How much will it cost, at $2.125 a meter? 29. How many meters of carpet 75cm wide will be required for a room 5.6" square? How wide a strip will have to be turned under? How much will the carpet cost, at $1.25 a meter? *Six widths would leave a surface 60cm wide to be covered. This surface would require another strip, of which a width of 200m would be "turned under." It is economy to select carpeting of the right width for the room. PAPERING AND PLASTERING. 208. The area of the four walls of a room is equal to that of a rectangle whose length is the perimeter of the room, and whose breadth is the height of the room. = Perimeter twice the length + twice the breadth. Area = perimeter x height. = 30. Find the area of the walls of a room whose length is 6.12m, breadth 5.05m, and height 3.5m? 31. How many rolls of paper 45cm wide and 8m long, allowing 11.199m for doors and windows, will be required to paper this room? 32. Find the cost of papering a room 8m long, 5.5m wide, and 4.5m high, with paper 50cm wide and 7.5m in a roll, at $1.25 a roll, put on? There is a base-board 25cm wide running round the room, and an allowance of 11am is made for doors and windows. 33. Find the cost of plastering this room, at $.50 a square meter. 34. Find the cost of papering a room 5.5m long, 4.8m wide, and 3.2m high, with paper 45cm wide, 7.5m in a roll, at $.875 a roll, put on, allowing 12m for base-board, doors, etc. 35. Find the cost of plastering this room, at $.45 a square meter. 36. Find the cost of papering a room 6m square and 3.5m high, with paper 45cm wide and 7.5m in a roll, at $.75 a roll, put on; and of putting on a border, at 5 cents per running meter. 37. Find the cost of plastering this room, at $.36 a square meter. 38. Find the cost of papering a room 13m long, 12m wide, and 7m high, with paper 45cm wide and 7.5m in a roll, at $1.50 a roll, put on; and of putting on a border, at $.30 a running meter, allowing 115m for baseboards, doors, etc. 39. Find the cost of plastering this room, at $.60 a square meter. BOARD MEASURE. 209. When boards are 25mm or less in thickness, they are sold by the square meter. Likewise, boards more than 25mm thick, plank and "dimension" lumber are sold by board measure. That is, by calculating the number of square meters of boards 25mm thick to which each piece is equivalent. Thus, a board 4m long, 25cm wide, and 25mm or less in thickness, is a meter, board measure; but a plank 4m long, 25cm wide, and 75mm thick, is three meters, board measure. For, since the plank is three times as thick as an ordinary board, it is equivalent to three boards, each 4m long and 25cm wide. If a board tapers regularly, its average width is found by taking one-half the sum of its end widths. How many meters, board measure: 40. In a board 8m long and 20cm wide? 41. In a joist 5m long, 25cm wide, and 75mm thick? 42. In a stick of timber 15m long and 40cm square? 43. In 2 joists 5m long, 27.5cm wide, and 50mm thick? 44. In 10 planks, each 4m long, 45cm wide, and 10cm thick and what is the value of these planks, at $25 a hundred meters? 45. In 25 box boards, each 4m long, 42cm wide, and 20mm thick? and what is their value, at $14 a hundred meters? Find the cost of: 46. Ten joists 4.5m long, 10cm wide, and 7.5cm thick, at $11 a hundred meters. 47. Thirty-six planks, each 4m long, 27.8cm wide, and 75mm thick, at $16 a hundred meters. 48. Three sticks of timber, each 8m long, 22.5cm wide, and 20cm thick, at $17.50 a hundred meters. 49. A board 8.25m long, 28cm wide at one end and 35cm at the other, and 31.25mm thick, at $.30 a meter? 50. A stick of timber 10m long, 25cm thick, 30cm wide at one end and 25cm wide at the other, at $14 a hundred meters. 51. The flooring for a two-story building 16m by 10.5; the flooring being 32mm thick, and worth $30 a hundred meters. 52. The flooring timbers for this building, the timbers being 25cm by 50mm, and placed on edge 30cm apart, and worth $11.50 a hundred meters. 53. The fencing to enclose a field 150m long and 75m wide; the posts are set 2.5m apart, and cost $.25 apiece; the fence is 5 boards high; the bottom board is 30cm, the top board 25cm, and the other three each 22.5cm wide, and the boards cost $13.25 a hundred meters. NOTE. Round logs are sold by board measure; .25 is deducted for slabs. A scale is used, the calipers of which are applied to the middle of the log, and the amount of boards for a given length is read off the scale. Large and heavy timber is sold by the ton; only .20 is allowed for slabs, and the amount is reckoned in cubic measure instead of board measure. MEASURES OF VOLUME. To find the volume of a rectangular solid. 210. In the figure represented in the margin, let the length contain 5, the breadth 3, and the height 7 linear centimeters. The base may be divided into square centimeters: there will be three rows of 5 square centimeters each; in all, 15 square centimeters. Upon each square centimeter may be placed a pile of 7 cubic centimeters; so that the solid will contain 15 x 7 cubic centimeters, that is, 3 x 5 x 7 cubic centimeters. Hence, Express the length, breadth, and height of a rectangular solid in the same linear unit; the product of these numbers will be its volume in cubic units of the same name as the linear unit of the edges. EXERCISE VI. 1. How many cubic centimeters in a block 9cm long by 7cm wide, and 6cm deep? 2. If wood is cut into 120cm lengths, and a pile is 43.7m long and 3. In a grain elevator is a bin 11.2m deep. How many hektoliters Hektoliter. 4. If a liter of grain weigh .81 of the weight of a liter of water, how much will the grain in that bin weigh? |