Find the other dimension: 7. Area 24 sq. ft., length 8 ft. 12. Area 56 sq. ch., length 8 ch. Find the circumferences of circles having the following diameters: NOTE.- Indicate the operation only. 27. 78 ft. 28. 19 ft. 29. 316.14 rd. 30. 189.68 ch. Written. Find areas: 31. Circumference 37.6992 ft., radius 6 ft. 32. Circumference 47.124 ft., diameter 15 ft. 33. Circumference 62.832 ft., diameter 20 ft. 34. Circumference 94.248 ft., diameter 30 ft. 35. Diameter 24 ft. 36. Radius 16 ft. 37. Circumference 50 ft. 38. Diameter 160 ft. 39. Radius 62 ft. 40. Circumference 314.16 ft. 41. How many square yards are there in a floor 24 ft. long and 15 ft. wide? 42. The base of a triangle is 20 ft. and the altitude 18 ft. What is the area? 43. The circumference of a circle is 31.416 ft. and its radius is 5 ft. What is its area? 44. When the diameter of a circle is 50 ft., what is the circumference? 45. When the radius is 6 ft., what is the circumference? 46. When the circumference is 78.54 ft., what is the radius? 47. Mr. Clark's farm is 35 ch. long and 25 ch. wide. How many acres does it contain? 48. A certain field is 70 rd. long and 65 rd. wide. How many acres are there in the field? 49. A piece of land is 65 rd. wide. How long must it be to contain 567 acres? 50. How many sods 10 inches square will be required to turf a lawn 100 ft. long and 50 ft. 6 in. wide? 51. A building lot measures 60 ft. in front. What must be its depth to contain of an acre? 52. How many tiles, each 8 in. square, will be required for the floor of a room 24 ft. by 30 ft.? 53. How many shingles will be required for a roof 45 ft. long, and each of its two sides 20 ft. wide, allowing 8 shingles to the square foot? 54. How many square yards of oil-cloth are needed to cover a floor 18 ft. by 24 ft. 6 in. ? 55. A owns a city lot 168 ft. long and 42 ft. wide. He of it for a lawn. How many square yards does the uses 56. How long will it take a man to mow the above lot, if it takes him a minute to run a 2-foot lawn-mower lengthwise of the lot? 57. A pony can reach 40 feet in any direction from the stake to which he is picketed. Over how many square rods of surface can he graze? 58. What is the diameter of a tree that is 10 ft. in circumference? 59. A basin measures 9 in. across the top and 6 in. across the bottom. How much farther around the top than around the bottom? 60. How many acres of land are enclosed by a circular mile track? 61. A landscape gardener lays off a circular grass-plot whose radius is one rod, and near it a semicircular plot having a radius two rods in length. Compare their areas. 62. If the area of a triangle is 9 acres and the base is 80 rods, what is the altitude? 63. Find the area of one gable end of a building 40 ft. wide, the ridge being 15 ft. above the eaves. 64. Find the area of a triangle whose altitude is 14 ft. and its base 12 ft. 65. Find the area of a triangle whose altitude is 4 in. and base 12 in. CARPETING ROOMS. 234. In making a carpet, the carpeting is cut from a roll into strips which are usually laid from end to end of the floor, or lengthwise. Sometimes the strips are laid across the room. 1. How much carpeting must I purchase to cover a room 6 yd. long and 4 yd. wide, strips running lengthwise? SOLUTION. It will be necessary to purchase as much carpeting as if the room were 5 yd. wide, the excess of yd. being turned under in the last strip. 1 strip contains 6 yd. 5 strips = 5 times 6 yd. = 30 yd. Ans. 2. How many yards must I purchase, if the strips are laid across the room? SOLUTION.-1 strip contains 4 yd. 6 strips = 6 times 4 yd. 281 yd. Ans. = 434 yds. 6 yd. ing to cover a room, on account of the waste in matching patterns. This diagram represents the floor in Example 1, in which the strips are laid lengthwise. Pupils should draw a similar diagram for each floor. NOTE. measure. Carpeting is sold by lineal yards or metres, not by square 3. A merchant bought a roll of carpet containing 74 yd. at 85 a yard, and sold it at $1.15 a yard. What was his profit ? 4. A roll of carpet yd. wide contains 60 yards. How many square yards of surface will it cover? 5. How many strips of carpet 3 ft. wide will cover a floor 15 ft. wide? 17 ft. wide? 18 ft. wide? 6. How many strips 27 in. wide are required for a floor 12 ft. wide? 14 ft. wide? 16 ft. wide? 7. If, in Example 5, the room is 16 ft. long, how many linear yards of carpet will be needed to cover the floor? 8. If, in Example 6, the room is 19 ft. long, how many yards will be required to cover the floor? 9. How many yards of ingrain carpet & yd. wide will be required for a floor 17 ft. wide and 20 ft. long, strips running across the room? 10. How much will a carpet cost at $.90 a yard to cover a floor 22 ft. long and 15 ft. wide, if the strips run crosswise, and no allowance is made for matching? 11. How many yards of carpet yd. wide will be required for a floor 20 ft. long and 15 ft. wide, if the strips run across the room? 12. How many yards of carpet 1 yd. wide will be required for a floor 18 ft. long and 14 ft. wide, strips running across the room? 13. How many yards of carpeting are needed to cover a floor 24 ft. long and 17 ft. wide, strips running lengthwise and yd. wide? 14. If my room is 161 ft. long and 12 ft. wide, how many yards of carpeting 24 inches wide must I buy, if in cutting 6 inches is allowed on each strip for matching? My room is 21 ft. 15. I wish to have a carpet woven. long and 17 ft. wide. How much carpeting, 34 inches wide, must I order to exactly cover the room, no allowance being made for matching? |