 | George Washington Hull - Geometry - 1897 - 408 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 - 376 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 - 468 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 - 324 pages
...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 - 232 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 - 450 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 - 404 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 - 424 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 - 398 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 - 498 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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Similar cylinders are to each other as the cubes of their altitudes, or as the cubes of the diameters of their bases. 
