0.00645

11. If 2 cu. in. of mercury weighs 1 lb., and 100 cu. in. of air weighs 31 gr., how many kilometers high must a column of air be to weigh as much as a column of mercury 29.388 in. high, standing on a base of the same area?

12. If a sprinter can run 0.0645 of a mile in 1.08 sec., how many meters can he run in a second? How many seconds will it take him to run 100m?

13. Two trains going in opposite directions pass each other in 3 sec. If their lengths are 260 ft. and 200 ft., respectively, and the first train is going at the rate of 80km an hour, what is the rate of the second train ?

14. If a cubic inch of water converted into steam will produce mechanical force sufficient to raise a weight of 2200 lb. one foot high, how many meters high would the conversion into steam of a cubic centimeter of water raise a weight of one kilogram?

15. If a man takes 100 steps of 0.7m each in a minute, how long will it take him to walk a distance of 28km ?

16. A lot of land containing 63a 21ca, worth $0.35 a square yard, is exchanged for a second lot containing 1ha 5a. What is the cost per ar of the second lot?

17. Light travels in 8 min. 13 sec. from the sun to the earth, 153,624,000km. What is the velocity of light in

miles per second ?

18. How many square feet of surface has a rectangular table that is 1.1m long and 0.85m wide ?

19. How many square meters of surface has a circular table that is 31 ft. in diameter ?

20. If sound travels 340m a second, how many feet distant is a cannon from a man who hears the report 13 sec. after he sees the flash?

21. How many square meters of zinc will be required to line a rectangular cistern, open at the top, 12 ft. long, 10 ft. wide, and 8 ft. deep?

22. A rectangular tank is 3m long, 21m wide, and 11m high, external measurement. If its sides are 0.1m thick, how many gallons of water will the tank hold?

23. If a cube of pine wood 11.2em on an edge weighs 2 lb., what is the specific gravity of the pine?

24. Find in kilograms the weight of water a cubical cistern will hold, 6 ft. on an edge.

25. Rain has fallen to the depth of half an inch. How many cubic meters of water has fallen on an acre of land?

26. How many centimeters will the water sink in a cylindrical cistern 7 ft. in diameter, if 310 gallons of water is pumped out?

27. How many square yards of tin are required to cover the roof of a hemispherical dome 12m in diameter ?

28. If a cubic inch of iron weighs 4 oz., what is the weight in kilograms of an iron ball 10cm in diameter ?

29. If a cubic inch of lead weighs 7 oz., what is the weight in kilograms of a lead pipe 3m long, 6cm in external diameter, if the pipe is 1cm thick?

30. Find the cost at $7.25 per meter of building a wall around a rectangular garden 90 ft. long and 55 ft. wide.

31. The minute hand of a clock is 0.5m long. How many feet does its point move in an hour?

32. A spherical shot 3 in. in diameter is melted and then cast into a cylinder 9cm in diameter. What is the height in centimeters of this cylinder?

33. What is the cost at $18 per 1000 ft. board measure of 4 beams, each 4.5m long, 7.5cm wide, and 5cm thick?

34. The radius of a cylindrical roller is 0.4m and its length is 2.15m. Find its volume in cubic feet.

35. A cylindrical cistern, the circumference of whose base is 2.2m, and whose depth is 2.1m, is four fifths filled with water. Find in gallons the volume of the water, and in pounds the weight of the water.

CHAPTER XI.

RATIO AND PROPORTION.

376. Ratio. The relative magnitude of two numbers is called their ratio, when expressed by the fraction that has the first number for its numerator and the second number for its denominator.

Thus, the ratio of 2 to 3 is expressed by the fraction .

377. Antecedent and Consequent. The terms of this fraction are called the terms of the ratio. The first term of a ratio is called the antecedent; the second term, the consequent.

Thus, in the ratio of 2 to 3, commonly written 2:3, the first term 2 is the antecedent, and the second term 3 is the consequent.

378. If both terms of a ratio are multiplied or both divided by the same number, the value of the ratio is not changed.

Thus, if the ratio 21:33 is multiplied by 6, the resulting ratio is

15:20, and the ratio 21:31 is equal to 15:20; for

1⁄2 reduced to its lowest terms = ratio of 21:31 is 3:4.

21

= 15 15. Since 20 3층 , the simplest expression for the

379. If the numerator and denominator of a fraction are interchanged, the fraction is said to be inverted; likewise, if the antecedent and consequent of a ratio are interchanged, the resulting ratio is the inverse of the given ratio.

Thus, if the fraction & is inverted the resulting fraction is ; and the inverse of the ratio 3:4 is 4: 3.

380. If two quantities are expressed in the same unit, their ratio is the same as the ratio of the two numbers by which they are expressed.

Thus, the quantity $5 is the same fraction of $11 as 5 is of 11; and, therefore, the ratio $5 : $11 equals the ratio 5:11.

381. Since ratio is simply relative magnitude, two quantities different in kind cannot form the terms of a ratio; and two quantities the same in kind must be expressed in a common unit before they can form the terms of a ratio.

Thus, no ratio exists between 5 tons and 30 days; and the ratio of 5 tons to 3000 pounds can be expressed only when both quantities are written as tons or as pounds.

382. Since ratios are mere. numbers, they may be compared.

383. Example. Which is the greater ratio, 5:7 or 12:18?

9. Find the ratio of 3 dry quarts to 2 pecks.

10. Find the ratio of 2500 lb. to 1 ton.

11. Find the ratio of a rectangular field 16 rd. long, 14 rd. wide to a rectangular field 14 rd. long, 12 rd. wide.

12. Find the ratio of a circle 1 in. in diameter to a circle 1 in. in radius.

384. When two ratios are equal the four terms are said to be in proportion, and are called proportionals.

=

Thus, 5, 3, 15, 9 are proportionals; for § 15.

385. Proportion. An expression of equality between two ratios is called a proportion.

A proportion is written by putting the sign of equality or a double colon between the ratios.

Thus, 5:3

=

15:9, or 5:3: 15:9, means, and is read, the ratio of 5 to 3 is equal to the ratio of 15 to 9.

386. Means and Extremes. The first and last terms of a proportion are called the extremes, and the two middle terms are called the means.

387. Test of a Proportion. When four numbers are in proportion, the product of the extremes is equal to the product of the means.

This is seen to be true by expressing the ratios in the form of fractions, and multiplying both by the product of the denominators.

Thus, the proportion 5:3 15:9 may be written § = 15; and if both are multiplied by 3 x 9, the result is 5 x 93 x 15.

388. Either extreme, therefore, is equal to the product of the means divided by the other extreme; and either mean is equal to the product of the extremes divided by the other mean. Hence, if three terms of a proportion are given, the fourth may be found.

389. Examples. 1. Find the missing term of the proportion 18:32 = 45 : ?.

2. Find the missing term of 20 : 24 =? : 30.