 | Encyclopedias and dictionaries - 1920 - 934 pages
...right triangles revolving round homologous perpendicular sides. The lateral areas, or the total areas, of two similar cones of revolution are to each other as the squares of their radii, or of their slant heights, or of their altitudes, and the volumes of similar... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 484 pages
...if the volume equals 80 ir. PROPOSITION XXXII. THEOREM 688. The lateral areas, or the total areas, of two similar cones of revolution are to each other as the squares of their altitudes, as the squares of their radii, or as the squares of their slant heights... | |
 | David Eugene Smith - Geometry, Solid - 1924 - 256 pages
...by the revolution of similar right triangles about corresponding sides, prove that the lateral areas of two similar cones of revolution are to each other as the squares of their altitudes. 4. In Ex. 3, consider the case of the total areas. 5. Consider Ex. 3 with... | |
 | Education - 1905 - 700 pages
...plane parallel to the base, the section is a polygon similar to the base. 4. Prove : The lateral areas of two similar cones of revolution are to each other as the squares of their altitudes. 5. Compute the area of a lune whose angle is 72 degrees on a sphere whose... | |
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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. 
