 | George Clinton Shutts - Geometry - 1905 - 410 pages
...the base of the cylinder of revolution. 581. COROLLARY II. The lateral areas of similar cylinders 0f revolution are to each other as the squares of their altitudes, or as the squares of the radii oj their bases. Let A, H, and R represent, respectively, the area, altitude, and the radius of the... | |
 | Isaac Newton Failor - Geometry - 1906 - 431 pages
...QED CONES PROPOSITION XXXIX. THEOREM 740 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... | |
 | Isaac Newton Failor - Geometry - 1906 - 440 pages
...464 CONES PROPOSITION XXXIX. THEOREM 740 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... | |
 | Edward Rutledge Robbins - Geometry - 1907 - 428 pages
...as the squares of their radii, or as the squares of their slant heights. II. The total areas are to each other as the squares of their altitudes, or as the squares of their radii, or as the squares of their slant heights. III. The volumes are to each other as the cubes... | |
 | Alan Sanders - Geometry - 1908 - 396 pages
...homologous legs as axes. PROPOSITION XIV. THEOREM 1046. The lateral or entire areas of two similar cones of revolution are to each other as the squares of...their bases; and their volumes are to each other as tJie cubes of their altitudes or as the cubes of the radii of their bases. [Proof similar to that of... | |
 | Webster Wells - Geometry - 1908 - 336 pages
...areas of two similar cones of revolution are to each other as the squares of their slant heights, or as the squares of their altitudes, or as the squares...; 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.... | |
 | Herbert Ellsworth Slaught, Nels Johann Lennes - Geometry, Solid - 1911 - 208 pages
...The lateral areas or the entire areas of two similar right circular cylinders are in the same ratio as the squares of their altitudes or as the squares of the radii of their bases. Suggestion. If h and h' are the altitudes, r and r' the radii, L and L' the lateral areas, and A and... | |
 | George Clinton Shutts - Geometry - 1912 - 392 pages
...expressed in terms of its altitude h and radius r by the formula V = rr2h. 637. COR. II. The volumes of two similar cylinders of revolution are to each other as the cubes of their altitudes and as the cubes of their radii (or their diameters). i. What must be the... | |
 | Clara Avis Hart, Daniel D. Feldman, Virgil Snyder - Geometry, Solid - 1912 - 216 pages
...4. § 590. 5. § 888. 6. Arg. 2. 7. § 355. 408 BOOK VIII PROPOSITION XVI. THEOREM 891. The volumes of two similar cylinders of revolution are to each other as the cubes of their altitudes, and as the cubes of the radii of their bases. H Given two similar cylinders... | |
 | Clara Avis Hart, Daniel D. Feldman - Geometry - 1912 - 504 pages
...the altitude, and B the radius of the base, of a cylinder. PROPOSITION XVI. THEOREM 891. The volumes of two similar cylinders of revolution are to each other as the cubes of their altitudes, and as the cubes of the radii of their bases. Given two similar cylinders... | |
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The lateral or total areas of two similar cones of revolution are to each other as the squares of their slant heights... 
