 The lateral or total areas of two similar cglinders of revolution are to each other as the 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...  The Elements of Solid Geometry - Page 30by William C. Bartol - 1893 - 95 pagesFull view - About this book
 | William Betz - Geometry - 1916 - 536 pages
...? == Trr'Vi' = /W = r*5 = A7"1' Why? 888. 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 ; and their volumes are to... | |
 | John Charles Stone, James Franklin Millis - Geometry, Solid - 1916 - 196 pages
...circular cylinder, then V = irRPH. The proof is left to the student. 382. Theorem. — The volumes of two similar cylinders of revolution are to each other as the cubes of the radii of their bases, or as the cubes of their altitudes. The proof is left to the student.... | |
 | William Betz, Harrison Emmett Webb - Geometry, Solid - 1916 - 214 pages
...r'h' r'2 h'2 PROPOSITION VI. THEOREM 888. 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 ; and their volumes are to... | |
 | Ernst Rudolph Breslich - Logarithms - 1917 - 408 pages
...altitude of a cylinder of revolution is 26. The radius of. the base is 24. Find the volume. 8. The volumes of two similar cylinders of revolution are to each other as the cubes of the altitudes, or as the cubes of the radii of the bases. Prove. 9. A cylindrical tank, Fig.... | |
 | Encyclopedias and dictionaries - 1920 - 934 pages
...generated by similar rectangles revolving round homologous sides. The lateral areas, and the total areas, of two similar cylinders of revolution are to each...altitudes, or as the squares of the radii of their bases. The volumes of similar cylinders of revolution are to each other as fhe cubes of their altitudes, or... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1918 - 486 pages
...equals 80 w. 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 ; and their volumes are to... | |
 | Encyclopedias and dictionaries - 1920 - 934 pages
...generated by similar rectangles revolving round homologous sides. The lateral areas, and the total areas, of two similar cylinders of revolution are to each...altitudes, or as the squares of the radii of their bases. The volumes of similar cylinders of revolution are to each other as the cubes of their altitudes, or... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 484 pages
...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 ; and their volumes are to... | |
 | David Eugene Smith - Geometry, Solid - 1924 - 256 pages
...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 " slant heights " substituted... | |
 | Education - 1905 - 694 pages
...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 diameter is 8 feet. 6. Compute... | |
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