| George Washington Hull - Geometry - 1897 - 398 pages
...the radii of their bases; and their volumes are to each other as the cubes of their slant heights, or **as the cubes of their altitudes, or as the cubes of the radii of their bases.** Given — S and s the lateral areas, T and t the total areas, Fand v the volumes, L and I the slant... | |
| Andrew Wheeler Phillips, Irving Fisher - Geometry - 1897 - 354 pages
...circular cylinder. Then V=irF?H. 859. COR. II. The volumes of two similar cylinders of revolution are to **each other as the cubes of their altitudes, or as the cubes of** their radii. V *RtII K* H ff H //3 R* OUTLINE PROOF : -=—-— = — x - = — x - = -— = — •... | |
| Arthur A. Dodd, B. Thomas Chace - Geometry - 1898 - 406 pages
...respective altitudes and r, r' the respective radii. Can you show that the volumes of these cones are to **each other as the cubes of their altitudes, or as the cubes of the radii of their bases,** or as the cubes of the diameters of their bases? Sug. Let V = volume of (I) and v = volume of (2).... | |
| Andrew Wheeler Phillips, Irving Fisher - Geometry - 1898
...i^' Therefore 966. COR. I 967, COR. II. The volumes of two similar cones of revolution are to eacli **other as the cubes of their altitudes, or as the cubes of the radii of their bases.** Hint. — The method of proof is the same as that followed in § 942. 068. Def. — The altitude of... | |
| James Howard Gore - Geometry - 1898 - 210 pages
...themselves are to each other as the cubes of their homologous edges. 432. COR. 2. Similar prisms are to **each other as the cubes of their altitudes, or as the cubes of** any other homologous lines. 433. COR. 3. Since the cylinder is the limit of a prism of infinite number... | |
| Webster Wells - Geometry - 1899 - 395 pages
...squares of their altitudes, or as the squares of the radii of their bases ; and their volumes are to **each other as the cubes of their altitudes, or as the cubes of the radii of their bases.** Given S and s the lateral areas, T and t the total areas, V and v the volumes, H and h the altitudes,... | |
| William James Milne - Geometry - 1899 - 384 pages
...the cubes of the radii of their bases ? Theorem. The volumes of similar cones of revolution are to **each other as the cubes of their altitudes, or as the cubes of the radii of their bases.** Data : Any two similar cones of revolution, whose altitudes are H and H', and the radii of whose bases... | |
| Webster Wells - Geometry - 1899 - 395 pages
...squares of their altitudes, or as the squares of the radii of their bases ; and their volumes are to **each other as the cubes of their altitudes, or as the cubes of the radii of their bases.** Given S and s the lateral areas, T and t the total areas, V and v the volumes, H and h the altitudes,... | |
| William James Milne - Geometry - 1899 - 384 pages
...radii? SOLID GEOMETRY. — BOOK IX. Theorem. The volumes of similar cylinders of revolution are to **each other as the cubes of their altitudes, or as the cubes of** their radii. Data : Any two similar cylinders of revolution, whose altitudes are H and H', and radii... | |
| George Albert Wentworth - Geometry - 1899 - 473 pages
...other as the squares of their altitudes, or as the squares of their radii ; and their volumes are to **each other as the cubes of their altitudes, or as the cubes of** their radii. Let S, S' denote the lateral areas, T, T' the total areas, V, V the volumes, H, H' the... | |
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