hektars, 7 ars, 17 centars, and 20 square decimeters, is written 25.07172 hektars, or 250717.2 square meters. 195. Write the following metric quantities as square meters and decimals. Ans. 3030303 sq m. Ans. 2.0202 sq m Solution. As 10000 square centimeters: 1 square meter, to reduce square meters to square centimeters we must move the decimal point four places to the right (Art. 63); that is, 8 sq m : = 80000 sq cm, Ans. 53. In 78456 sq mm how many square decimeters? how many square meters? 54. In 75 sq km how many hektars? how many square dekameters square meters? 55. Reduce 7.875 Ha to square meters. 56. Reduce 843.21 sqm to ars; to hektars. 197. A Rectangle is a plane (or flat) surface bounded by four straight lines and having all its angles equal. 198. The figure is called rectangular, and the angles right angles. 199. A Square is a rectangle whose sides are equal. 2 x 1 cm 2 x 2 cm 200. To find the area of a rectangle. B C Let A B C D be a rectangle whose base AD is 5 centimeters in length, and whose altitude A B is 3 centimeters. (The figure is drawn on a scale of 1 to 2.) If A D is divided into 5 equal parts and A B into 3, and lines are drawn through A D the points of division, the rectangle will be divided into squares, each containing 1 square centimeter; and the rectangle will evidently contain 5 × 3, or 15, of these squares; that is, its area = = (5 × 3) square centimeters = 15 square centimeters. Therefore, The area of a rectangle is the product of its length and breadth. 201. The area of a rectangle divided by the length will give the breadth, and the area divided by the breadth will give the length. 202. Written Exercises. 57. In a rectangular field 200 meters long and 56 meters broad how many ars? 11200 sqm=112 ars, Ans. 58. How many sq. meters in a floor 6.8 m long and 4.5 m wide ? 59. How many meters of carpeting 0.6 m wide will be needed to cover this floor? 60. At 5 mills a square decimeter of sheet tin what will 5 sqm cost? 61. If a square meter of land cost $8, what will an ar cost? 62. At 10 cents a square meter what will it cost to paint a rectangular surface 25.5 m long and 10.7 m wide? 63. How many bricks, each 20 cm long and 10 cm wide, will it take to pave a sidewalk 3.3 m wide, 1.7 long? Km 64. How many shingles will cover a roof 28 m by 15m, if each shingle covers a space 15 cm by 10 cm ? 65. What will it cost to cement a cellar 13.5 m by 9 m at $0.65 a square meter? 203. CUBIC MEASURE. The units of this table are obtained by cubing (taking three times as a factor) the units of the table of Linear Measure. 204. In measuring wood a cubic meter is sometimes called a ster (st). 205. Since the scale is 1000 (10 x 10 × 10), three places are required for each denomination. Thus, 2 cum, 2 is written 2.002002 cu m 2 cu dm cu cm 206. Write the following metric quantities as cubic meters and decimals. = = 1 cubic meter, to reduce cubic Solution. As 1000 cubic decimeters meters to cubic decimeters we must move the decimal point three cu dm, Ans. places to the right (Art. 63); that is, 12.87 cu m = 12870 cu dm, 72. Reduce 32500 cu dm to cubic meters. 73. Reduce 8 cum to cubic centimeters. 74. Reduce 875 cu cm to cubic decimeters; to cubic meters. 210. To find the volume of a rectangular prism. Let ABCD, EFGH be the rectangular prism whose base is a rectangle 5 centimeters from A to D, and 3 from A to B, and whose altitude AE is 4 centimeters. (The figure is drawn on a scale of 1 to 2.) cm E N M K. A F D G The rectangle ABCD contains (5×3) qem (Art. 200). If parallel to the base ABCD a plane is passed through the point K, one centimeter from A, it will evidently cut off 15 cubic centimeters, that is, (5 × 3 ×1) cubic centimeters. In like manner, if a plane passes through M parallel to the base, it will cut off 15 more; and so on. tangular prism contains (5 × 3 × 4) cubic cubic centimeters. Therefore, That is, the reccentimeters = 60 The volume of a rectangular prism is equal to the product of its three dimensions. 211. The volume of a rectangular prism divided by the area of its base will give the altitude; the volume divided by the area of one end will give the length; and the volume divided by the area of one side will give the breadth or width. 212. Written Exercises. 75. How many cubic meters in a box 1.25 m long, 1.13 m wide, and 0.8m deep? 76. How deep must a box be to contain 6 cu m 2.13 x 2.13m ? if the top is 77. How many cubic meters in a wall 25 m long, 3.4m high, and 268 thick? mm 78. How many sters in a pile of wood 25 m long, 1.25m wide, and 2m high? 79. How many cubic meters of earth must be removed to dig a ditch 75.4m long, 83 cm wide, and 44 cm deep? 80. At $0.85 a cum what would it cost to dig a cellar 13.3 m long, 11.5m wide, and 2.3 m deep? 81. How many bricks 20 by 10 by 5 solid wall 75 m long, 2.5 m high, and 55 cm cm will it take to build a thick? 82. What will it cost for the bricks to build this wall if bricks are $8.50 a thousand? |