152 21. If a bushel of corn weigh 56 lb., what is the value of 6 T. 12 cwt. of corn at 63 cents a bushel? 22. The difference in time between two places on the earth's equator is 4 hr. 35 min. 30 sec.; what is the distance in miles between the places if a degree is equal to 694 miles? 23. If the moon revolves around the earth in 27 da. 7 hr. 42 min., over how many degrees of its orbit does it pass in 22 da. 18 hr. 25 min.? 24. A and B bought 400 bu. 3 pk. of wheat for $240.45; if A pays $103.05, and B $137.40, how many bushels should each receive? 25. If the sides of a field are, respectively, 22 ch. 63 li., 24 ch. 963 li., and 27 ch. 3933 li., what is the length of the longest rail possible that can be used in making a fence around it without cutting or overlapping the rails, and how many rails will be required if the fence is 5 rails high? 26. If a rail weighs 21 pounds to the foot, how many tons will be required to lay 3 miles of railway? 27. An opera-glass cost $18.50; find its cost in English money if a pound is worth $4.8665. 28. A French-plate mirror cost $40.75; find its cost in German money if a mark is worth 23.85 cents. 29. If a cubic foot of water weighs 1000 oz., and mercury is 13.596 times as heavy as water, what is the weight in pounds of 216 cubic inches of mercury? 30. What decimal of a lb. avoirdupois is a fb Troy? 31. A vessel filled with water weighs 60 pounds: a mass of gold is thrown into it which displaces 5 lb. of water; how much do the vessel and its contents now weigh if gold is 19.4 times as heavy as water? 32. Express 6 3 2 3 29 4 gr. in avoirdupois weight. 33. If a stick 5 ft. 4 in. high cast a shadow 3 ft. 6 in. long, how high is a building whose shadow is 120 ft. 9 in. at the same time of the day? 34. How many days from the 4th of March, 1889, to the 4th of July, 1890? 35. A locomotive runs 81 miles in 2 hr. 14 min.; in what time will it run from Lancaster to Philadelphia, a distance of 69 miles, at the same rate? 36. If a bushel of wheat weighs 60 pounds, what is the value of A's crop of wheat, which weighs 8 T. 14 cwt., at 56 cents a bushel? 37. If a franc is worth 19.3 cents, what is the value in francs of £3 8 s. 4 d. when a pound is worth $4.8665? 38. A mass of copper weighs 88 cwt. 49 lb. 8 oz., and an equal mass of water weighs 10 cwt. 5 lb. 10 oz.; the copper is how many times as heavy as the water? 39. If A starts at the equator and travels due north 3000 miles, what latitude does he reach, allowing 69 miles to a degree? 40. Reduce 145 rd. 3 yd. 1 ft. 8 in. to the decimal of a mile. 41. What cost 3 bbl. of sugar, each weighing 2 cwt. 12 lb. 10 oz., if 1.26 cwt. cost $7.40? 42. What cost 12 lb. 11 oz. of drugs if 5 lb. 9 oz. cost $22.25? 43. Since noon the sun has seemed to pass over 20° 20′ 20′′; what time is it? 44. If B travels 40 mi. 150 rd. 3 yd. in 8 hr. 20 min., how far will he travel in 12 hr. 50 min.? 45. A 5-gallon cask containing vinegar lacks 1 pints of being full; what is the quantity of vinegar in the cask worth at 8 cents a quart? 46. A grain-dealer's scales are 25 pounds in a ton below the legal standard; how much does he gain fraudulently from the sale of 5 car-loads of wheat, each containing 240 bags of 174 pounds each, true weight, at 56 cents a bushel, reckoning 60 pounds to the bushel? SECTION VII. PRACTICAL MEASUREMENTS. MEASURES OF SURFACES. 139. A Surface is that which has length and breadth without thickness. THE RECTANGLE. 140. A Rectangle is a plane figure having four sides and A Square. four right angles; as, a slate, a door, etc. The Dimensions of a rectangle are its length and breadth. A rectangle has two bases; the side upon which it seems to stand is the lower base, and the side opposite the upper base. The Altitude of a rectangle is the perpendicular distance between its bases. A Rectangle. A Square is a rectangle whose sides are all equal. The Perimeter of a rectangle is the sum of its sides. The Area of a rectangle is the number of square units it contains. A B Thus, in the rectangle ABCD the area is the number of small squares it contains, which is equal to the number in each row multiplied by the number of rows, and this is equal to the number of linear units in the length multiplied by the number in the breadth. Hence the RULE. I. To find the area of a rectangle, multiply the length by the breadth. II. To find either side of a rectangle, divide the area by the other side. WRITTEN EXERCISES. 1. How many square feet in a yard 30 feet long and 20 feet wide? 2. How many square yards in a floor 33 feet long and 24 feet wide? 3. How many square rods in a field 120 rods long and 80 rods wide? 4. How many acres in a field 240 rods long and 120 rods wide? 5. How many acres in a field 15 chains long and 8 chains wide? 6. What is the width of a field 80 rods long which contains 12 acres? 7. How many square yards in a floor 16 ft. 6 in. long and 12 ft. 8 in. wide? 8. How many square yards in the sides of a room 24 ft. long, 20 ft. wide, and 12 ft. high? 9. A field is 10 chains long and 60 rods wide; how many acres does it contain? 10. How many chains long must a field 10 ft. wide be to contain an acre? 11. What will it cost to pave a sidewalk 75 ft. long and 6 ft. wide at 21 cts. a square foot? 12. What will be the cost of a concrete walk 120 ft. long and 4 ft. wide at 44 cts. a square yard? 13. What will it cost to cement the cellar of a house 40 ft. long and 24 ft. wide at 30 cts. a square yard? RULE. I. To find the area of a triangle, multiply the base by one-half the altitude. II. To find the base or altitude of a triangle, divide the area by one-half the other dimension. |