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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. "
Elements of Geometry and Trigonometry: With Notes - Page 187
by Adrien Marie Legendre - 1822 - 367 pages
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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...
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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....
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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

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...
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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,...
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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,...
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Plane and Solid Geometry

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...
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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
...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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Elementary Geometry, Plane and Solid: For Use in High Schools and Academies

Thomas Franklin Holgate - Geometry - 1901 - 462 pages
...homologous sides. 6. Show that the volumes of two similar right circular cones are in the same ratio as the cubes of their altitudes, or as the cubes of the radii of their bases. 8. Show that the lateral area of the frustum of a right circular cone is equal...
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