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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. "
Mathematical Dictionary and Cyclopedia of Mathematical Science Comprising ... - Page 146
by Charles Davies, William Guy Peck - 1859 - 592 pages
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Elements of Geometry

George Washington Hull - Geometry - 1897 - 398 pages
...the radii of their bases; 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. Given — S and s the lateral areas, T and t the total areas, Fand v the volumes, L and I the slant...
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Elements of Geometry

Andrew Wheeler Phillips, Irving Fisher - Geometry - 1897 - 354 pages
...circular cylinder. Then V=irF?H. 859. COR. II. The volumes of two similar cylinders of revolution are to each other as the cubes of their altitudes, or as the cubes of their radii. V *RtII K* H ff H //3 R* OUTLINE PROOF : -=—-— = — x - = — x - = -— = — •...
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Plane and Solid Geometry: Inductive Method

Arthur A. Dodd, B. Thomas Chace - Geometry - 1898 - 406 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
...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 - 210 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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The Essentials of Geometry

Webster Wells - Geometry - 1899 - 395 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 - 384 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 the radii of whose bases...
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The Essentials of Geometry

Webster Wells - Geometry - 1899 - 395 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 - 384 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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Plane and Solid Geometry

George Albert Wentworth - Geometry - 1899 - 473 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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