 | William Frothingham Bradbury - Geometry - 1872 - 262 pages
....5235. 5).}, Cor. 2. As in these equations J n- and -J n are constant, the volumes of spheres vary as the cubes of their radii, or as the cubes of their diameters. 1. How many square feet in the convex surface of a right prism whose altitude is 2 feet, and whose... | |
 | William Chauvenet - Geometry - 1872 - 382 pages
...whence D s = (2.R) S — SR 3 , 48. Corollary II. The volumes of two spheres are to each other as_ the cubes of their radii, or as the cubes of their diameters. PROPOSITION XV.—THEOREM. 49. The solid generated by a circular segment revolving about a diameter... | |
 | Adrien Marie Legendre - Geometry - 1874 - 500 pages
...by D, we shall have It equal to $D, and IP equal to ±-D3, and consequently, hence, the volumes of spheres are to each other as the cubes of their radii, or as the cubes of their diameters. ' Scholium. If the figure EBDF, formed by drawing lines from the extremities of the arc BD perpendicular... | |
 | William Chauvenet - Geometry - 1875 - 390 pages
...Or, if D is the diameter of the sphere, whence Ds = (2.R)3 = &R", 48. Corollary II. The volwrtes of two spheres are to each other as the cubes of their radii, or as the cubes ofr their diameters. PROPOSITION XV.— THEOREM. A 49. The solid generated by a circular segment revolving... | |
 | Lorenzo Fairbanks - 1875 - 472 pages
...Multiply the surface by | of the diameter, or -J- of the cube of the diameter by 3.1416. The solidities of spheres are to each other as the cubes of their radii or diameters. EXAMPLES. 1. What is the solidity of a sphere whose diameter is 18 inches ? 2. The diameter... | |
 | William Guy Peck - Conic sections - 1876 - 412 pages
...proved. surface is equal to 4.TR2 ; consequently its volume is equal to 4xR2 x £R, or to |aR». Cor. 2. Any two spheres are to each other as the cubes of their radii. Cor. 3. The volume of a spherical sector is equal to the zone which forms its base, multiplied by one•third... | |
 | J. G - 1878 - 408 pages
...by their heights. r2 h r72* h'' (8) The volumes of (a) similar cglinders or (6) similar cones are to each other as the cubes of their radii, or as the cubes of their heights. '.' The cylinders are similar, -= -,. T h :. By substituting this value of ^ in the above... | |
 | William Henry Harrison Phillips - Geometry - 1878 - 236 pages
...Hence vol. of a sphere = f «R3; or, if D denotes the diameter, vol. of a sphere = i »D". COR. 2. Two spheres are to each other as the cubes of their radii, or diameters. COR. 3. The volume of a spherical sector is equal to the product of the zone which forms... | |
 | Isaac Sharpless - Geometry - 1879 - 282 pages
...^R 3 • and since E = %D, R* = %IP; hence F = ^Z> 3 . Corollary 2. — Spheres are to one another as the cubes of their radii, or as the cubes of their diameters. Scholium. — A similar demonstration will prove that the volume of a spherical sector is equal to... | |
 | Charles Scott Venable - 1881 - 380 pages
...of the sphere, then V = surface of zone x |R = 2TrRH x ^R, or, v = f TrR'H. COR. 1. The volumes of two spheres are to each other as the cubes of their radii, or as the cubes of their diameters. COR. 2. The volume of a spherical wedge is equal to the. lune v.'hich forms its base multiplied by... | |
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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. 
