 | Arthur A. Dodd, B. Thomas Chace - Geometry - 1898 - 468 pages
...r2 h. 573. Cor. II. Can you show that the volumes of any two similar cylinders of revolution are to each other as the cubes of their radii, or as the cubes of their altitudes ? Sug. 1. (l)^- = p. Why? y ft v=^r*- h; *u ' ~~«?-" Complete proof. 574. Cor. III. Can... | |
 | William James Milne - Geometry - 1899 - 404 pages
...and V' = f 7nR'3; V : V' = 4 7rfl3 : -4 77-S'3 = fl3 : R'3 = D3:D'3; do 1 that is, i/te volumes of two spheres are to each other as the cubes of their radii, or as the cubes of their diameters. 746. Cor. II. The volume of a spherical pyramid is equal to the product of its base by one third of... | |
 | Webster Wells - Geometry - 1899 - 424 pages
...the solid generated by sector OAB as a limit, see Appendix, p. 391. 378 679. Cot. IV. The volumes of two spheres are to each other as the cubes of their radii, or as the cubes of their diameters. (The proof is left to the pupil.) 680. Cor. V. The volume of a spherical pyramid is equal to the area... | |
 | William James Milne - Geometry - 1899 - 396 pages
...spheres. Then, § 744, V = %irR\ and v' = ^R'3; V: V' = that is, the volumes of two spfteres are to each other as the cubes of their radii, or as the cubes of their diameters. 746. Cor. II. The volume of a spherical pyramid is equal to the product of its base by one third of... | |
 | George Albert Wentworth - Geometry, Solid - 1899 - 246 pages
...sphere is equal to 4 -rrR2 X$R; that is, f irHs, or % 7rZ>3. (D = diameter.) 846. COR. 2. The volumes of two spheres are to each other as the cubes of their radii. For V:V' BOOK VIII. SOLID GEOMETRY. 848. COR. 4. The volume of a spherical sector is equal to one third... | |
 | James Howard Gore - Geometry - 1899 - 266 pages
...by one-third of the radius, or 537. COR. 1. Since (by 533) and V=\*LP. 538. COR. 2. The volumes of two spheres are to each other as the cubes of their radii. 539. COR. 3. The volume of a spherical sector is equal to the area of the zone which forms its base... | |
 | William James Milne - Geometry - 1899 - 398 pages
...v = £ irR3, and v' = f iTR" ; V: V' = irR that is, the volumes of two spheres are to each other ay the cubes of their radii, or as the cubes of their diameters. 746. Cor. II. The volume of a spherical pyramid is equal to the product of its base by one third of... | |
 | George Albert Wentworth - Geometry, Solid - 1899 - 248 pages
...squares of their slant heights ; and their volumes art 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,... | |
 | George Albert Wentworth - Geometry - 1899 - 496 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,... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1902 - 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. n {— -7J— ' Hyp. £, 6", are the lateral areas; T, T, the total areas, V, V, the volumes,... | |
| |
The volumes of two spheres are to each other as the cubes of their radii, or as the cubes of their diameters. 
