RULE.-I. Divide the volume by the product of the terms proportional to the three dimensions, and extract the cube root of the quotient. II. Multiply the root thus obtained by each proportional term; the products will be the corresponding sides. 2. What are the dimensions of a rectangular box whose volume is 3000 cu. ft., and its dimensions are to each other as 2, 3, and 4? 3. A pile of bricks in the form of a parallelopiped contains 30720 cu. feet, and the length, breadth, and height are to each other as 3, 4, and 5. What are the dimensions of the pile? SIMILAR SOLIDS. 935. Similar Solids are such as have the same form, and differ from each other only in volume. PRINCIPLES.-1. The volumes of similar solids are to each other as the cubes of their like dimensions. 1. If the volume of a ball 3 inches in diameter is 27 cu. in., what is the volume of a ball 7 inches in diameter. OPERATION.-33: 73: : 27 cu. in. : x 343 cu. in., = volume. 2. The like dimensions of similar solids are to each other as the cube roots of their volumes. 3. If the diameter of a ball whose volume is 27 cu. in. is 3 in., what is the diameter of a ball whose volume is 343 cu. inches? OPERATION.-27: 343 :: 33: x3 = 343; 343 = 7 in., diameter. 936. 1. What is the edge of a cube whose entire surface is 1050 sq. feet, and what is its volume? 2. What must be the inner edge of a cubical bin to hold 1250 bu. of wheat? 3. How many gallons will a cistern hold, whose depth is 7 ft., the bottom being a circle 7 feet in diameter and the top 5 feet in diameter ? 4. What is the value of a stick of timber 24 ft. long, the larger end being 15 in. square, and the less 6 in., at 28 cents a cubic foot? 5. If a cubic foot of iron were formed into a bar an inch square, without waste, what would be its length? 6. If a marble column 10 in. in diameter contains 27 cu. ft., what is the diameter of a column of equal length that contains 81 cu. ft.? 7. How many board feet in a post 11 ft. long, 9 in. square at the bottom, and 4 in. square at the top? 8. The surface of a sphere is the same as that of a cube, the edge of which is 12 in. Find the volume of each. 9. A ball 4.5 in. in diameter weighs 18 oz. Avoir.; what is the weight of another ball of the same density, that is 9 in. in diameter ? 10. In what time will a pipe supplying 6 gal. of water a minute fill a tank in the form of a hemisphere, that is 10 ft. in diameter? 11. The diameter of a cistern is 8 feet; what must be its depth to contain 75 hhd. of water? 12. How many bushels in a heap of grain in the form of a cone, whose base is 8 ft. in diameter and altitude 4 feet? GAUGING. 937. Gauging is the process of finding the capacity or volume of casks and other vessels. A cask is equivalent to a cylinder having the same length and a diameter equal to the mean diameter of the cask. To find the mean diameter of a cask (nearly), Add to the head diameter, or, if the staves are but little curved. .6, of the difference between the head and bung diameters. To find the volume of a cask in gallons, Multiply the square of the mean diameter by the length (both in inches) and this product by .0034. 1. How many gallons in a cask whose head diameter is 24 inches, bung diameter 30 in., and its length 34 inches? OPERATION.-24 + (3024 × 3) = 28 in., mean diameter. 282 × 31 × .003490.63 gal., capacity. 2. What is the volume of a cask whose length is 40 inches, the diameters 21 and 30 in., respectively. 3. How many gallons in a cask of slight curvature, 3 ft. 6 in. long, the head diameter being 26 in., the bung diameter 31 in. ? METRIC SYSTEM. 940. The Metric System of weights and measures is based upon the decimal scale. 941. The Meter is the base of the system, and is the one tenmillionth part of the distance on the earth's surface from the equator to either pole, or 39.37079 inches. 942. From the Meter are made the Are (air), the Stere (stair), the Liter (leeter), and the Gram; these constitute the primary or principal units of the system, from which all the others are derived. 943. The Multiple Units, or higher denominations, are named by prefixing to the name of the primary units the Greek numerals, Deka (10), Hecto (100), Kilo (1000), and Myra (10000). 944. The Sub-multiple Units, or lower denominations, are named by prefixing to the names of the primary units the Latin numerals, Deci (†), Centi (1), Milli Todo). Hence, it is apparent from the name of a unit whether it is greater or less than the standard unit, and also how many times. 945. The Meter is the unit of length, and is equal to 39.37 in., nearly. The Meter, like our yard, is used in measuring cloths and short distances. The Kilometer is commonly used for measuring long distances, and is about of a common mile, 946. The Are is the unit of land measure, and is a square whose side is 10 meters, equal to a square dekameter, or 119.6 sq. yards. 947. The Square Meter is the unit for measuring ordinary surfaces; as flooring, ceilings, etc. TABLE. 100 Sq. Millimeters, sq.mm.=1 Sq. Centimeter 948. The Stere is the unit of wood or solid measure, and is equal to a cubic meter, or .2759 cord. 949. The Cubic Meter is the unit for measuring ordinary solids; as excavations, embankments, etc. TABLE. 1000 Cu. Millimeters, cu. mm. = 1 Cu. Centimeter 1 Cu. Decimeter MEASURES OF CAPACITY 950. The Liter is the unit of capacity, both of liquid and of Dry Measures, and is a vessel whose volume is equal to a cube whose edge is one-tenth of a meter, equal to 1.05673 Liquid Measure, and .9081 qt. Dry Measure. |