7. What is the side of a steel plate that will contain 150 square inches? PROCESS √150=√25×6=5√6=5x2.4495 12.2475 (in.) Ans. Take as the factors of 150, 25 (the largest square) and 6. Write the square root of 25 outside the radical, leaving 6 inside. Take the value of √6 from the table. NOTE.-5√6 is read "5 times the square root of 6." Since the squareroot sign is also called a radical, the foregoing expression is sometimes read as "5 radical 6." 8. Give the values of the following: a. √120 = ? b. √200=? c. √350=? 9. An acre contains 4840 square yards. How many yards long is a square field containing one acre? SECTION XIV GOVERNMENT AND BUSINESS STANDARDS Weights and Measures Owing to the variations in the practices of individuals in the United States, the several states, cities, etc., have found it necessary from time to time to fix definite standards both as to quantities and qualities. In some cities the purchaser of a quart of milk is reasonably certain of obtaining an article containing not less than 3% of butter fat, that of inferior grade being subject to seizure by the Board of Health. In some localities a loaf of bread must weigh a pound; in others, a label giving the weight must be affixed. In many places storekeepers are required to weigh out 15 pounds of potatoes to a customer asking for a peck, the use of a measure not being permitted. As a protection to honest dealers some states have enacted laws as to the capacity of a barrel, the legal weight to the bushel of grain, etc. The following table gives a few standard weights prevailing in most of the states: Whether the bushel will hold only 58 pounds of wheat by actual measurement, or 62 pounds, the seller is paid the bushel price for every 60 pounds delivered. The basis of all our weights and measures is the yard, an exact copy of the standard yard being kept in Washington and at the various state capitals. The length of the yard bears a definite ratio to the length of a pendulum beating seconds at the sea level. When the yard is obtained, a cube can be made, each side measuring a foot. The weight of the water of a certain temperature occupying a cubic foot is 1000 ounces. A measure that will hold 231 cubic inches is a gallon; one that will contain 2150.42 cubic inches is a bushel. = A hand, used in measuring the height of horses = 4 in. A fathom, used in measuring depths at sea 6 ft. A knot, used in measuring distances at sea = 1 geographical mile = 1.15 statute miles. Diameters of buttons are expressed in lines, sizes of type in points. A gill is pt. The capacity of cisterns, reservoirs, etc., is sometimes expressed in barrels (bbl.) of 311 gallons each, or in hogsheads (hhd.) of 63 gallons each. Barrels and hogsheads used in commerce vary in capacity. A gallon contains 231 cu. in. In making a rough estimate of the capacity of a tank, etc., a cubic foot is taken as the equivalent of 71⁄2 gallons. A bushel contains, approximately, 2150.4 cu. in. In estimating the capacity of a bin, etc., a bushel is taken as the equivalent of 11 cu. ft. Square Measure 144 square inches (sq. in.) 30 square yards 160 square rods 640 acres = 1 square foot (sq. ft.) = 1 square yard (sq. yd.) = = 1 square rod (sq. rd.) = 1 acre (A.) = 1 square mile (sq. mi.) A square mile of land is called a section. Roofing, slating, and flooring are often estimated by the square of 100 sq. ft. Cubic Measure 1728 cubic inches (cu. in.) = 1 cubic foot (cu. ft.) 27 cubic feet = 1 cubic yard (cu. yd.) A cord of wood contains 128 cu. ft. A perch of stone or masonry is taken as 24 cu. ft. in some localities; in others as 16 cu. ft. In making an agreement to do work at a certain price per perch, its equivalent should be specified. The long ton is the only one employed in England. In this country it is used in selling coal and ore at the mines, and in custom house calculations. In some cities dealers are required to sell coal by the long ton. Troy Weight 24 grains (gr.) = 1 pennyweight (pwt.) Troy weight is used in weighing gold and silver. Weights of large quantities are expressed in ounces; of small quantities in grains. The pennyweight is employed chiefly in denoting the weight of gold jewelry, which is frequently sold by the pennyweight. Gold and silver are rendered harder by the admixture of other metals. Gold coin consists of 90 parts gold, 9 parts silver, and 1 part copper. Coin silver consists of 9 parts silver and 1 part copper. The fineness of gold is frequently expressed in carats, 24 carats denoting pure gold. Gold 22 carats fine means that it consists of 22 parts of gold and 2 parts of alloy; gold 18 carats fine contains 18 parts of gold and 6 parts of alloy. The value of pure gold is practically permanent, being determined by the value of gold coin; that is, a piece of gold of the weight and fineness of a 20-dollar gold coin is worth $20. The price of silver fluctuates. Written Problems 1. The last government report gives the production of pure gold as 21,380,000 ounces for the year, worth $441,930,000. Find the value per ounce. 2. The production of pure silver for the same time was 203 million ounces worth 109 million dollars. its value per ounce ? What was 3. Twenty years ago the production of pure silver was 120 million ounces worth 112 million dollars. What was its value per ounce twenty years ago? 4. Twenty years ago the production of pure gold was 6 million ounces worth 123 million dollars. What was the value per ounce ? |