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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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New Plane Geometry

Webster Wells - Geometry - 1908 - 329 pages
...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 heights,...
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Elements of Plane and Solid Geometry

Alan Sanders - Geometry - 1908 - 396 pages
...altitudes or as the squares of the radii 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 § 1022.] 1047. EXERCISE. The volume of one of two similar cones of revolution...
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Plane Geometry Developed by the Syllabus Method

Eugene Randolph Smith - Geometry, Plane - 1909 - 424 pages
...parallel. Show also that this is not true if the lines AB and A'B' are perpendicular to plane P. 522. Similar cylinders are to each other as the cubes of their altitudes, or as the cubes of the diameters of their bases. 523. Show that the projections of parallel lines on the same plane are parallel,...
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Solid Geometry

George C. Shutts - 1913 - 212 pages
...Complete the demonstration. 638. 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 (or their diameters'). Proof. Left to the pupil. See § 633. 7. Which generates the greater...
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Plane and Solid Geometry, Suggestive Method

George Clinton Shutts - Geometry - 1913 - 494 pages
...radius r by the formula V — 638. 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 (or their diameters) . Proof. Left to the pupil. See § 633. 7. Which generates the greater...
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Plane and Solid Geometry

George Albert Wentworth, David Eugene Smith - Geometry - 1913 - 496 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. Given two similar cylinders of revolution, / and /' denoting their lateral areas, t and...
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Plane and Solid Geometry

Webster Wells, Walter Wilson Hart - Geometry - 1916 - 490 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. Hypothesis. S and s are the lateral areas, T and t are the total areas, V and v are the volumes, H...
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Plane and Solid Geometry

Webster Wells, Walter Wilson Hart - Geometry - 1916 - 504 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. Hypothesis. $ and s are the lateral areas, T and t the total areas, F~and v are the volumes, L and...
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Solid Geometry

William Betz, Harrison Emmett Webb - Geometry, Solid - 1916 - 214 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. Given two similar cylinders of revolution, with lateral areas / and /', total areas t...
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Plane and Solid Geometry

William Betz - Geometry - 1916 - 536 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. Given two similar cylinders of revolution, with lateral areas / and /', total areas t...
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