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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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Elementary Geometry

William Chauvenet - 1893 - 340 pages
...COROLLARY I. For a cone of revolution, the proposition may be formulated, V — faR'.If. 30. COROLLARY II. Similar cones of revolution are to each other as the...altitudes, or as the cubes of the radii of their bases. EXERCISE. Theorem.—A frustum of any cone is equivalent to the sum of three cones whose common altitude...
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The Elements of Geometry

Webster Wells - Geometry - 1894 - 394 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. Let S and denote the lateral areas, T and t the total areas, V and v the volumes, L and l the slant...
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Plane and Solid Geometry: Suggestive Method

George Clinton Shutts - Geometry - 1894 - 412 pages
...base of the cylinder of revolution. 381. 584. COROLLARY II. The volumes of similar cylinders oj revolution are to each other as the cubes of their altitudes, or the cubes of the radii of their bases. altitude, and radius of the base of one cylinder, and V, H,...
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Plane and Solid Geometry: Suggestive Method

Charles Ambrose Van Velzer, George Clinton Shutts - Geometry - 1894 - 416 pages
...The truth of the theorem may be expressed by the formula CONES. 503. COROLLARY II. The lateral areas of two similar cones of revolution are to each other as the squares of their slant heights, or the squares of their altitudes, or the squares of the radii of their...
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Elements of Geometry: Plane and Solid

John Macnie - Geometry - 1895 - 386 pages
...altitude ; then, since B = ir • R1, V = IT . R* . H. 677. COR. 2. The volumes of similar cylinders of revolution are to each other as the cubes of their altitudes or radii. For if V and V' be the volumes of two similar cylinders of revolution, B and B' the radii of...
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Elements of Geometry

Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 554 pages
...Therelore H. QE 966. COR. I. If the base of the cone is a circle of radius /?, 967. COR. II. The volumes of two similar cones of revolution are to each other as the cubes of their altitudes, or as tlic cubes of the radii of their bases. If int. — The method of proof is the same as that followed...
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Syllabus of Geometry

George Albert Wentworth - Geometry - 1896 - 68 pages
...a cone of revolution, and R is the radius of the base, 674. The lateral areas, or the total areas, of two similar cones of revolution are to each other as the squares of their altitudes, or of their radii ; and their volumes are to each other as the cubes of...
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Elements of Geometry

Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 564 pages
...similar right triangles about homologous sides. 959. COR. III. The lateral areas, or the 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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Elements of Geometry

Andrew Wheeler Phillips, Irving Fisher - Geometry - 1897 - 376 pages
...the volume of a 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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Elements of Geometry

George Washington Hull - Geometry - 1897 - 408 pages
...the radius of the base. PROPOSITION X. THEOREM. 630. The lateral areas, and also the entire 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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