EXERCISES. Find the cube root of: 1. 614,125. 8. 2,000,376. 15. 592,704. CUBE ROOT OF COMMON AND DECIMAL FRACTIONS. 1. What is the cube root of 27? 0 4= }; for } x } } = (3)' = 24 FORMULA. = By rule: Numerator ở Denominator 2. What is the cube root of .8? Not .2, for .2 X .2 X.2 = .008. .800'000 (.92 + 729 24300 71000 540 49688 4 21312, Rem. 24844 Hence 3.8 .92 +. In such cases annex ciphers, and make periods from the point toward the right. 5. Find the cube root of: 6. = 4. 8. 1498 10. 177 8000 63367 = VOLUME. Volume of a cube = side. Therefore: Ø volume = side of cube. PROBLEMS. 1. A cubical cistern contains 1331 solid feet. What is the length of one side of the cistern? 2. A cubical pedestal contains 373,248 cu. in. What is the length of one of its sides ? 3. A cubical box contains 474,552 cu. in. What is the area of one of the surfaces of the box? 4. How much paper will cover the six surfaces of a cubical box whose volume is 27 cu. ft. ? a 5. What is the depth of a cubical box that will hold a bushel ? 6. A wagon-box holds 100 bu. The length is twice the width and the width and depth are equal. Find the dimensions. 7. Find the cost, at 83 cts. per square yard, of lining the inside of a cubical box holding 900 gal. of water. 8. Find the height of a cubical pile of wood containing 179 cords. SIMILAR FIGURES. 1. Similar figures have the same shape, but differ in size. 2. Figures are either surfaces or solids. 3. A surface has dimensions and area. 4. A solid has dimensions and volume. 5. The relation of similar figures is in accordance with the following general principles : Similar Surfaces. 1. The areas of similar surfaces are to each other as the squares of their like dimensions. 2. The like dimensions of similar surfaces are to each other as the square roots of their areas. PROBLEMS. 1. Two surfaces having the same shape are to each other as 114 to 36. What is the ratio of their lengths ? Process. 12 : L. :1. = V 144 : V 36. 6. 2: 1. Hence the ratio of their lengths is 2:1. a 2. The radius of a certain circle is 5 ft. What is the radius of another circle containing twice the area of the first? Suggestion : 5: R. =V1: V 2. 3. The surfaces of two bodies having the same shape are as 100 : 25. What is the ratio of their widths ? 4. If the area of a circle, whose diameter is 2 ft., is 6.2832 sq. ft., what is the diameter of a circle whose area is 25.1328 a sq. ft.? Suggestion : 25.1328 = 4 times 6.2832. 5. A farmer has a field 50 rd. wide by 80 rd. long, which contains 25 A. Find the dimensions of a similar field containing 16.81 A. 6. If a horse tied to a stake by a rope 8.79 rd. long can graze upon 12 A. of land, how long must the rope be that he may graze upon 6 A.? 7. If a pipe whose diameter is 1.5 in. fills a cistern in 5 hours, in what time will a pipe whose diameter is 3 in. fill the same cistern ? 8. A half-inch pipe discharges a barrel of water in a certain time. How much will a 2-in. pipe discharge in the same time? 9. If a 1-in. pipe discharges 1 gal. in 45 seconds, how much will a 2-in. pipe discharge in 60 seconds ? 10. A rectangular piece of land has a width of 160 ft. and is valued at $1200. What is the value of a similar piece of land having twice the length and breadth ? a Similar Solids. 1. The volumes of similar solids are to each other as the cubes of their like dimensions. 2. The like dimensions of similar solids are to each other as the cube roots of their volumes. PROBLEMS. 1. Of two spheres, one is 1000 times the size of the other. If the diameter of the smaller is 6 inches, how many feet are in the diameter of the larger ? 2. The diameter of a ball weighing 32 lb. is 6 in. What is the diameter of a ball weighing 4 lb. ? 3. The diameters of two spheres are respectively 4 and 12 in. The larger sphere is how many times the smaller ? 4. If a 2-in. globe of gold is worth $500, what is the value of a 6-in. globe of gold ? 5. If the diameter of the sun is 112 times as long as that of the earth, how much greater is the mass of the sun than that of the earth? 6. If the diameter of the moon is 2000 mi. and that of the earth is 8000 mi., what is the ratio of their volumes ? 7. The weights of two cylinders of the same shape are as 27 to 64. What is the ratio of their lengths ? Process. 3: 4. a 8. If a log 11 ft. in diameter contains 35 cu. ft., what is the diameter of a log of the same length that contains. 105 cubic feet? 9. If a pyramid of hay 12 ft. high contains 8 tons, how high is a similar pyramid that contains 60 tons ? a |