 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 394 pages
...other as the squares of their radii, or as the squares of their altitudes ; and their volumes are to each other as the cubes of their radii, or as the cubes of their altitudes. __ H H' Hyp. S, S', are the lateral areas; T, T, the total areas, V, V', the volumes, R,... | |
 | Thomas Franklin Holgate - Geometry - 1901 - 462 pages
...F"= Jr-x4ar2=|B-r3. (Art. 662.) 669. COROLLARY II. The volumes of two spheres are in the same ratio as the cubes of their radii, or as the cubes of their diameters. EXERCISES ELEMENTARY GEOMETRY [CHAP. IX Spherical pyramid DEFINITIONS 670. A spherical pyramid is a... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1901 - 396 pages
...If V denotes the volume, R the radius, and D the diameter of the sphere, 770. COB. 2. The volumes of two spheres are to each other as the cubes of their radii. 771. COR. 3. The volume of a spherical pyramid is equal to the area of its base multiplied by one-third... | |
 | Arthur Schultze - 1901 - 392 pages
...squares of their slant heights ; and their volumes are to each other as the cubes of their altitudes, as the cubes of their radii, or as the cubes of their slant heights. Hyp. 8, S' are the lateral areas, T, T' the total areas, V, V' the volumes, H, H' the... | |
 | William Estabrook Chancellor - Arithmetic - 1902 - 178 pages
...b s or z 3 : <?. The volumes of cubes are to each other as the cubes of their edges. The volumes of two spheres are to each other as the cubes of their radii, or as the cubes of their diameters, or as the cubes of their circumferences. 1. A sphere, 3 in. in diameter, weighs 8 Ib. What is the weight... | |
 | Middlesex Alfred Bailey - Algebra - 1902 - 336 pages
...— Wi 216 SOLUTION OF PROBLEMS (6) Solve by proportion. From geometry, we know that the volumes of two spheres are to each other as the cubes of their radii. » : », : : Л3 : 27, ОГ n = ^ jy> «:о'::B3: 64, or »» = — Rs v : V= : : B3 : 125, or Oi =... | |
 | George Albert Wentworth - Geometry, Solid - 1902 - 248 pages
...equal to QED 4 irR 2 X$R; that is, J -nR*, or £ TrZ> 8 . (D = diameter.) 846. COR. 2. The volumes of two spheres are to each other as the cubes of their radii. For V: V 848. COR. 4. The volume of a spherical sector is equal to one third the product of the zone... | |
 | George Albert Wentworth - Geometry, Solid - 1902 - 246 pages
...squares of their slant heights; and their volumes are to each other as the cubes of their altitudes, as the cubes of their radii, or as the cubes of their slant heights. Let S and S' denote the lateral areas, T and T' the total areas, V and V' the volumes,... | |
 | Alan Sanders - Geometry - 1903 - 396 pages
...,^ surface sphere Whence vol. spher. pyramid = base x ,j radius.] 1199. COROLLARY IV. The volumes of spheres are to each other as the cubes of their radii, or as the cubes of their diameters. 1200. EXERCISE. The number of cubic feet in the volume of a certain sphere is the same as the number... | |
 | Fletcher Durell - Geometry, Solid - 1904 - 232 pages
...other as the squares of their radii, or as the squares of their altitudes; and their volumes are to each other as the cubes of their radii, or as the cubes of their altitudes. ii a' Given two similar cylinders of revolution having their lateral areas denoted by S... | |
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The volumes of two spheres are to each other as the cubes of their radii, or as the cubes of their diameters. 
