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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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Schultze and Sevenoak's Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 488 pages
...if the volume equals 80 IT. PROPOSITION XXXII. THEOREM 688. 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

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

John Charles Stone, James Franklin Millis - Geometry, Solid - 1916 - 196 pages
...bottom and 1 in. in diameter at the PYRAMIDS AND CONES 417. Theorem. — The lateral or the total areas of two similar cones of revolution are to each other as the squares of the slant heights, the altitudes, or the radii of the bases ; and their volumes are to each...
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Plane and Solid Geometry

William Betz - Geometry - 1916 - 536 pages
...irr^h r2/; i^ A8 '*" ? == Trr'Vi' = /W = r*5 = A7"1' Why? 888. 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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Solid Geometry

William Betz, Harrison Emmett Webb - Geometry, Solid - 1916 - 214 pages
...Trrh + 2 77T2 = 2 7i r'h' r'2 h'2 PROPOSITION VI. THEOREM 888. 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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Solid Geometry

Fletcher Durell, Elmer Ellsworth Arnold - Geometry, Solid - 1917 - 220 pages
... 569. Why? QED PROPOSITION XII. THEOREM 631. Similar cones of revolution are to each other as thi cubes of their altitudes, or as the cubes of the radii of their bases. Given two similar cones of revolution with their volumes denoted by V and F7, their radii by r and...
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Solid Geometry Developed by the Syllabus Method

Eugene Randolph Smith - Geometry, Solid - 1918 - 232 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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The Encyclopedia Americana: A Library of Universal Knowledge, Volume 25

Encyclopedias and dictionaries - 1920 - 934 pages
...right triangles revolving round homologous perpendicular sides. The lateral areas, or the total areas, of two similar cones of revolution are to each other as the squares of their radii, or of their slant heights, or of their altitudes, and the volumes of similar...
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Schultze and Sevenoak's Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1918 - 486 pages
...base if the volume equals 80 w. PROPOSITION XXXII. THEOREM 688. 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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