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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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Plane and Solid Geometry

George Albert Wentworth - Geometry - 1904 - 496 pages
...the base, B = 7T.B2. 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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Plane and Solid Geometry

Fletcher Durell - Geometry - 1911 - 553 pages
...and $ = 4, find $, T and F. CONES PROPOSITION X. THEOREM 724. The lateral areas, or the total areas, of two similar cones of revolution are to each other as the squares of their radii, or as the squares of their altitudes, or as the squares of their slant heights;...
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Solid Geometry

Fletcher Durell - Geometry, Solid - 1904 - 232 pages
...JB=4, find S, T and V. CONES ^. PROPOSITION X. THEOREM 724. The lateral areas, or the total areas, of two similar cones of revolution are to each other as the squares of their radii, or as the squares of their altitudes, or as the squares of their slant heights;...
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Manual of Examinations for Engineering Positions in the Service ..., Parts 1-9

Myron H. Lewis - Civil service - 1906 - 838 pages
...MECHANICS. 6. Assuming the formula for determining the solidity of a cone as proved, show that the volumes of two similar cones of revolution are to each other as the cubes of their heights. 7. Given two adjacent sides, a and b, of a triangle, and also the included angle...
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Plane and Solid Geometry

Isaac Newton Failor - Geometry - 1906 - 440 pages
...E, then B = irR2. 464 CONES PROPOSITION XXXIX. THEOREM 740 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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Plane and Solid Geometry

Isaac Newton Failor - Geometry - 1906 - 431 pages
...= B x H. 264 QED CONES PROPOSITION XXXIX. THEOREM 740 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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Plane and Solid Geometry

Edward Rutledge Robbins - Geometry - 1907 - 428 pages
...the squares of their altitudes or as the squares of the radii of their bases. III. The volumes are to each other as the cubes of their altitudes or as the cubes of the radii of their bases. Given : Two similar cylin. H ders of revolution whose lateral areas = L and I ; whose total areas =...
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Plane and Solid Geometry

Edward Rutledge Robbins - Geometry - 1907 - 428 pages
...or as the squares of their radii, or as the squares of their slant heights. III. The volumes are to each other as the cubes of their altitudes, or as the cubes of their radii, or as the cubes of their slant heights. Given: Two similar cones of revolution, whose...
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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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