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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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New Plane and Solid Geometry

Webster Wells - Geometry - 1908 - 338 pages
...and R the radius of the base, of a circular cone, PROP. X. THEOREM 506. The lateral or 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 Geometry Developed by the Syllabus Method

Eugene Randolph Smith - Geometry, Plane - 1909 - 424 pages
...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

Clara Avis Hart, Daniel D. Feldman, Virgil Snyder - Geometry, Solid - 1912 - 216 pages
...bases and equal altitudes. Find the ratio of their volumes. PROPOSITION XVIII. THEOREM 897. The volumes of two similar cones of revolution are to each other as the cubes of 'their altitudes, as the cubes of their slant heights, and as the cubes of the radii of their bases. Given two similar...
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Plane and Solid Geometry: Suggestive Method

George Clinton Shutts - Geometry - 1912 - 392 pages
...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 shape of a piece of paper...
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Solid Geometry

Clara Avis Hart, Daniel D. Feldman, Virgil Snyder - Geometry, Solid - 1912 - 220 pages
...5. 888. 6. Arg. 2. 7. 355. 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 of revolution with their...
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Solid Geometry

Clara Avis Hart, Daniel D. Feldman, Virgil Snyder - Geometry, Solid - 1912 - 230 pages
...about homologous sides as. axes. PROPOSITION XI. THEOREM 878. The lateral areas, and the total areas, of two similar cones of revolution are to each other as the squares of their altitudes, as the squares of their slant heights, and as the squares of the radii...
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Plane and Solid Geometry

Clara Avis Hart, Daniel D. Feldman - Geometry - 1912 - 504 pages
...about homologous sides as axes PROPOSITION XI. THEOREM 878. The lateral areas, and the total areas, of two similar cones of revolution are to each other as the squares of their altitudes, as the squares of their slant heights, and as the squares of the radii...
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Solid Geometry

George C. Shutts - 1913 - 212 pages
...Why? Therefore— 4. 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 - 498 pages
...its altitude h and 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 - 500 pages
...and the ra,dius of the base. PROPOSITION XXIX. THEOREM 614. 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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