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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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Chauvenet's Treatise on Elementary Geometry

William Chauvenet - Geometry - 1887 - 322 pages
...this proposition may be formulated, Corollary II. Similar cones of revolution are to each other aa the cubes of their altitudes, or as the cubes of the radii of their bases. PROPOSITION VIII. The area of the surface generated by a straight line revolving about an axis in its...
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The Elements of Plane and Solid Geometry ...

Edward Albert Bowser - Geometry - 1890 - 393 pages
...radius of the base is R, we have . (439) 780. COR. 2. The volumes of similar cones of revolution are to each other as the cubes of their altitudes, or as the cubes of the radii of their boses. (759) EXERCISES. 1. Eequired the lateral area and volume of a right circular cone whose altitude...
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The Elements of Plane and Solid Geometry: With Numerous Exercises

Edward Albert Bowser - Geometry - 1890 - 393 pages
...1! X H' ~ H' R1 R" (758) - V ~ R"H' Therefore, the volumes of similar cylinders of revolution are to each -other as the cubes of their altitudes, or as the cubes of their radii. THE CONE. DEFINITIONS. 760. A conical surface is a surface generated by the motion of...
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Elementary Geometry

William Chauvenet - 1893
...proposition may be formulated, V — faR'.If. 30. COROLLARY II. Similar cones of revolution are to each other as the cubes of their 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 SOLID GEOMETRY

WILLIAM C. BATOL, A.M., - 1893
...ELEMENTS OF SOLID GEOMETRY. EXERCISES. 151. THEOREM. The volume of two similar cones of revolution are to each other as the cubes of their altitudes, or as the cubes of the radii of their bases. 152. THEOREM. The surfaces, Lateral or total, of two similar cones of revolution are to each other...
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The Elements of Geometry

Webster Wells - Geometry - 1894 - 378 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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Elements of Geometry: Plane and Solid

John Macnie - Geometry - 1895 - 374 pages
...; then, since B = TT . R-, (398) V = % TT . R- . H. 694. COR. 2. Similar cones of revolution are to each other as the cubes of their altitudes, or as the cubes of their radii. For if R and R' are the radii of two similar cones of revolution, H and 7/ their altitudes,...
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Elements of Geometry

Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 540 pages
...the cone is a circle of radius R, 967. COR. II. The volumes of two similar cones of revolution are to each other as the cubes of their altitudes, or as the cubes of the radii of their bases. H int. — The method of proof is the same as that followed in 942. 968. Def. — The altitude of...
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Elements of Geometry

Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 540 pages
...circular cylinder. Then V^TrK'H. 042. 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. A" V OUTLINE PROOF: — = IP H _ '" ~~~ * H _ ~THE CONE 943. Def. — A pyramid is inscribed...
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Elements of Geometry

Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 540 pages
...the cone is a circle of radius R, 967. COR. II. The volumes of two similar cones of revolution are to each other as the cubes of their altitudes, or as the cubes of the radii of their bases. Hint. — The method of proof is the same as that followed in 942. 968. Def. — The altitude of...
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