CLOTH MEASURE. (Art. 152.) 45. How many quarters in 45 yards? SQUARE MEASURE. (Art. 153.) 51. In 175 square rods and 7 yards, how many feet? 52. In 56 acres and 3 roods, how many square feet? 53. In 1275 square miles, how many acres ? 54. How many square rods in 25640 feet? 55. How many acres in 1865 roods? 56. How many acres in 2135680 yards ? 163. The area of a floor, a piece of land, or any surface which has four sides and four right angles, is proved by multiplying its length and breadth together. Obs. 1. The area of a figure is the superficial contents or space contained within the line or lines, by which the figure is bounded. It is reckoned in square inches, feet, yards, rods, &c. 57. How many square feet are there in a table which is 4 feet long and 3 feet wide ? Suggestion. Let the table be represented by the subjoined figure, the length of which is divided into 4 equal parts, and the breadth into 3 equal parts, which we will call linear feet. Now it is plain that the table will contain as many square feet as there are squares in the given figure. But QUEST.-163. How do you find the area or superficial contents of a surface having four sides and four right angles ? Obs. What is meant by the term area? How is it reckoned? What is a figure which has four sides and four right angles, called ? the number of squares in the figure is equal to the number of equal parts (linear feet) which its length contains, repeated as many times as there are equal parts (linear feet) in its breadth ; that is, equal to 4 x3, or 12. The table therefore contains 12 square feet. Obs. 2. A figure which has four sides and four right angles, like the preceding, is called a Rectangle, or Parallelograin. 58. What is the area of a garden which is 8 rods long and 5 rods wide ? Ans. 40 square rods. 59. How many square feet in a floor, 18 feet long and 17 feet wide ? 60. How many square yards in a ceiling, 20 feet long and 18 feet wide ? 61. What is the area of a field which is 36 rods long and 25 rods wide ? 62. How many acres are there in a piece of land 80 rods long and 48 rods wide ? CUBIC MEASURE. (Art. 154.) 63. In 75 cubic feet, how many inches ? 64. In 37 tons of round timber, how many inches ? 65. In 28124 cubic feet, how many tons of square timber? 66. In 16568 cubic feet of wood, how many cords? 67. In 65 cords of wood, how many cubic feet? 164. The solidity, or cubical contents of boxes of goods, piles of wood, &c., are found by multiplying the length, breadth, and thickness together. 68. How many cubic inches are there in a box, whose length is 30 inches, its breadth 18, and its depth 15 inches? Ans. 8100 in. 69. How many cubic inches in a block of marble, 43 inches long, 18 inches broad, and 12 inches thick ? Quest.-164. How are the cubical contents of a box of goods, a pile of wood, &c., found? 70. How many cubic feet in a room, 16 feet long, 15 feet wide, and 9 feet high? 71. How many cubic feet in a load of wood, 8 feet long, 4 feet wide, and 31 feet high? 72. How many cubic feet in a pile of wood, 16 feet long, 6 feet wide, and 5 feet high? How many cords ? 73. How many cords of wood in a pile, 140 feet long, 4 feet wide, and 6 feet high? WINE MEASURE. (Art. 155.) 74. In 4624 gills, how many gallons ? 75. In 24260 quarts, how many hogsheads? 76. How many pints in 15 hogsheads, 20 gallons ? 77. How many gills in 40 barrels ? BEER MEASURE. (Art. 156.) 78. How many barrels of beer in 5000 pints ? 79. How many hogsheads in 7800 quarts ? 80. How many quarts in 25 hogsheads and 7 gallons ? 81. How many pints in 110 gallons, 3 qts. and 1 pt. ? DRY MEASURE. (Art. 157.) 82. Reduce 536 bushels, 3 pecks, to quarts. TIME. (Art. 158.) 86. In 15 days, 6 hours, 9 minutes, how many seconds ? 87. In 365 days and 6 hours, how many minutes ? 88. How many seconds in a solar year ? 89. Allowing 365d. 6h. to a year, how many minutes has a person lived who is 21 years old ? 90. How many hours in 568240 seconds ? CIRCULAR MEASURE. (Art. 159.) 95. In 75 degrees, how many seconds ? 96. In 8 signs, 15 degrees, how many minutes ? 97. In 12 signs, how many seconds ? 98. In 86860 seconds, how many degrees ? 99. In 567800 minutes, how many signs ? 100. In 25000000 seconds, how many signs ? COMPOUND NUMBERS REDUCED TO FRACTIONS. Ex. 1. Change 7s. 6d. to the fraction of a pound. Reducing the 12 12 78. 6d. to pence, (Art. 161, 1,) we Numerator 90d. Denominator 240d. have 90d., which Ans. = 2, or . is the numerator of the fraction. Then reducing £1 to the same denomination as the numerator, we have 240d., which is the denominator. Thus is the fraction required. This may be reduced to lower terms. =24, or . (Art. 120.) Hence, 90 240 165. To reduce a compound number to a common fraction. First reduce the given compound number to the lowest denomination mentioned for the numerator ; then reduce a UNIT of the denomination of the required fraction to the same denomination as the numerator, and the result will be the denominator. Obs. When the given number contains but one denomination, it of course requires no reduction. 2. Reduce 3s. 7d. 2 far. to the fraction of £1. Ans. £20, or £ 3. Reduce 9d. 3 far. to the fraction of ls. 4. What part of a bushel is 3 pecks and 5 qts. ? 480 QUEST.-165. How is a compound number reduced to a common fraction? 5. What part of a peck is 5 qts. and 1 pt. ? 6. What part of a gallon is 3 qts. 2 pts. and 3 gills ? 7. What part of i gallon is 1 pt. and 1 gill ? 8. What part of i hogshead is 2 gals. and 4 qts. ? 9. What part of 1 ton is 5 cwt. and 2 qrs. ? 10. What part of i hundred weight is 2 qrs. and 7 lbs.? 11. What part of 1 quarter is 1 lb. and 5 oz. ? 12. What part of 1 mile is 45 rods? 13. What part of 1 mile is 10 fur. and 35 rods ? 14. What part of i league is 1 m. 1 fur. and 1 r. ? 15. What part of 1 yard is 2 qrs. and 3 nails ? 16. What part of £i is 1 penny? Ans. £210: 17. What part of £1 is of a penny? Ans. 7o. Note.—The lowest denomination mentioned in this example is thirds of a penny. Hence, £1 must be reduced to thirds of a penny for the denominator, and 2, the given number of thirds, will be the numerator. 18. What part of £1 is 58 shillings? Ans. 23 FRACTIONAL COMPOUND NUMBERS Ex. 1. Reduce of £1 to shillings and pence. Operation. Multiply the numerator by 20, to 3 eighths £. reduce it to shillings, as in reduc20 tion. (Art. 161, I.) £{ x 205.03. 8)60 or 7s. and 4 remainder. Again, mulshil. 7, and 4 Rem. tiplying the remainder 4 by 12, we have 48; and 48=8=6d. The 12 quotients, 7s. and 6d. are the an8)48 swer required. Hence, Pence 6. Ans. 7s. 6d. |