The volumes of two spheres are to each other as the cubes of their radii, or as the cubes of their diameters. Solid Geometry - Page 319by Walter Burton Ford, Charles Ammerman - 1913 - 107 pagesFull view - About this book
| Dana Pond Colburn - Arithmetic - 1855 - 396 pages
...diameter, or it equals £ of the cube of the diameter multiplied by 3.1416* («.) The solidities of spheres are to each other as the cubes of their radii or diameters. (<,.) The solidities of similar solids are to each other as the cubes of their like dimensions.... | |
| Dana Pond Colburn - Arithmetic - 1856 - 392 pages
...diameter, or it equals £ of the cube of the diameter multiplied by 3.1416* (n.) The solidities of spheres are to each other as the cubes of their radii or diameters. • See foot note, page 34.3. (o.) The solidities of similar solids are to each other as... | |
| Thomas Dick - 1857 - 878 pages
...amounts to thirty. This radius, and that, of the orbit of Uranus, are in the ratio of 1 to 49 ; and the volumes of two spheres are to each other as the cubes of their radii. If, therefore, we adopt the hypothesis of the equal distribution of comets in all the regions of our... | |
| James Stewart Eaton - Arithmetic - 1857 - 376 pages
...all similar solids are to each other as the cubes of their homologous lines ; thus, the solidities of two spheres are to each other as the cubes of their radii, as the cubes of their diameters, or as the cubes of' their circumferences, etc., etc. ; the solidities... | |
| Dana Pond Colburn - 1858 - 288 pages
...3.1416 = J of 1728 times 3.1416 = 288 times 3.H16 cu. ft. = 904.7808 cu. ft. (m.) The solidities of spheres are to each other as the cubes of their radii or diameters. ILLUSTRATION. — A sphere of 3 ft. radius contains 27 as many cubic feet as a sphere of... | |
| Dana Pond Colburn - Arithmetic - 1860 - 388 pages
...diameter, or it equals -g- of the cube of the diameter multiplied by 3.1416* ^ (n.) The solidities of spheres are to each other as the cubes of their radii or diameters. * See foot note, page 343. (n ) The solidiiios of similar solids are to each other as the... | |
| Smithsonian Institution - Science - 1883 - 818 pages
...as the volume of the latter is to the volume of the former. But these volumes or solid contents vary as the cubes of their radii, or as the cubes of their distances from the vertex. Therefore the force of gravity varies inversely as the cubes of the distances.... | |
| James Stewart Eaton - Arithmetic - 1868 - 356 pages
...the volumes of all similar bodies are to each other as the cubes of their homologous lines ; thus, the volumes of two spheres are to each other as the cubes of their radii, as the cubes of their diameters, or as the cubes of their circumferences, etc., etc. ; the volumes... | |
| Albert Taylor Bledsoe, Sophia M'Ilvaine Bledsoe Herrick - Periodicals - 1870 - 512 pages
...thirty-seven. This radius and that of the orbit of Neptune are in the ratio of one to seventy-eight. But the volumes of two spheres are to each other as the cubes of their radii. If, then, we adopt the hypothesis of an equal distribution of comets in our system, — and no reason... | |
| William Chauvenet - Geometry - 1871 - 380 pages
...V=±xR* X \R = $xR*. Or, if D is the diameter of the sphere, whence D3 = (2R)3 = 8R3, 48. Corollary II. The volumes of two spheres are to each other as the...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... | |
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