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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. "
The Elements of Solid Geometry - Page 46
by William C. Bartol - 1893 - 95 pages
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Elements of Geometry

Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 562 pages
...similar right triangles about homologous sides. 959. COR. III. The lateral areas, or the total 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 of the radii...
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Plane and Solid Geometry: Inductive Method

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)....
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Elements of Geometry: Geometry of space

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...
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Plane and Solid Geometry

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...
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Plane and Solid Geometry: Inductive Method

Arthur A. Dodd, B. Thomas Chace - Geometry - 1898 - 468 pages
...proposition. Can you make an arithmetical formula for this proposition ? EXERCISES. 498. The lateral areas of two similar cones of revolution are to each other as the squares of their slant height, or the squares of their altitudes, or the squares of the radii of their...
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The Essentials of Geometry

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,...
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The Essentials of Geometry

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,...
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Plane and Solid Geometry

William James Milne - Geometry - 1899 - 404 pages
...of the cubes of their radii? SOLID GEOMETRY. — BOOK IX. Theorem. The volumes of simitar 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...
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Solid Geometry, Volumes 6-9

George Albert Wentworth - Geometry, Solid - 1899 - 246 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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Plane and Solid Geometry

George Albert Wentworth - Geometry - 1899 - 500 pages
...of the base, B = -irR2. 463 PROPOSITION XLI. THEOREM. 726. 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...
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