CUBE ROOT OF IMPERFECT CUBES. 231. When a number is an imperfect cube, periods of ciphers may be annexed and the process continued as far as desired. 40. Find the cube root of 5. CUBE ROOT OF FRACTIONS. 232.-47. Find the cube root of 3. 37 7 V8 .956+, Ans. If the denominator is a perfect cube and the numerator is not, divide the approximate cube root of the numerator by the cube root of the denominator. If the denominator is not a perfect cube, reduce the fraction to an equivalent fraction having a perfect cube for a denominator. The Edge of a cube is equal to the cube root of its contents. WRITTEN EXERCISES. 1. Find the edge of a cubical box which contains 216000 cubic inches. 2. Find the entire surface of a cubical chest whose contents are 15625 cubic inches. 3. What is the edge of a cube which contains as much as a solid 7 ft. long, 42 in. wide, and 21 in. high? 4. A miller has a cubical box with which he takes toll; what are its dimensions, if it contains of a bushel? 5. What are the dimensions of a cubical box that will hold 20 bushels? 6. What is the depth of a cubical cistern that will hold 1000 gallons of water? 7. B has a cubical bin whose contents are 175616 cubic inches; what will it cost to line the bottom and sides, at 10 cents a square foot? 234. Similar Volumes. Similar Volumes are those which have the same form, but differ in volume. It is proved in Geometry that 1. Similar volumes are to each other as the cubes of their like dimensions. 2. The like dimensions of similar volumes are to each other as the cube roots of their volumes. These principles may be illustrated thus: WRITTEN EXERCISES. 1. If a ball 4 in. in diameter weighs 10 lb., what does a ball 12 in. in diameter weigh? Since the cubes of the like dimensions of similar solids are to each other as their volumes, then 43, the diameter of the first cubed, is to 123, the diameter of the second cubed, as 10 lb., the weight of the first, is to the From which we find the weight of the larger 2. If a ball 5 in. in diameter weighs 24 lb., what is the diameter of a similar ball which weighs 81 lb.? 3. If a stack of hay 8 ft. in diameter weighs 15 tons, what is the diameter of a similar stack which weighs 120 tons? 4. If a globe of gold 2 inches in diameter is worth $500, what is the value of a globe 6 inches in diameter? 5. The diameters of two similar cisterns are to each other as 1 to 8; what is the relation of their contents? 6. If a bin 10 ft. long holds 50 bushels, how long is a similar bin which holds 400 bushels? 7. If a bin 15 ft. long and 10 ft. wide contains 800 cubic feet, what are the dimensions of a similar bin which contains 2700 cubic feet? 8. If a bar of metal 3 ft. long, 2 ft. wide, and 1 ft. thick weighs 2700 lb., what are the dimensions of a similar bar which weighs 6400 lb.? 9. If the surfaces of two spheres are to each other as 4 to 9, what is the relation of their contents? 10. If the volumes of two spheres are to each other as 250 to 128, what is the relation of their surfaces? 11. If a log 3 ft. in diameter contains 70 cubic feet, what is the diameter of a log of the same length that contains 210 cubic feet? SECTION XI. MENSURATION. 235. Mensuration is the process of computing the lengths of lines, the areas of surfaces, and the volumes of solids. LINES. 236. A Line is that which has length only. Straight Line. Curved Lines. Parallel Lines. A Straight Line is a line that does not change its direction. A Curved Line is a line that changes its direction at every point. Parallel Lines are lines which have the same direction. ANGLES. 237. An Angle is the figure formed by two straight lines which meet at a point; as, CDA, CDB, EFG, HKL. |