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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. "
Elements of Geometry and Trigonometry: With Notes - Page 187
by Adrien Marie Legendre - 1822 - 367 pages
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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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The Elements of Solid Geometry

William C. Bartol - Geometry, Solid - 1893 - 106 pages
...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...
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Elementary Geometry

William Chauvenet - 1893 - 336 pages
...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...
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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,...
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Elements of Geometry: Plane and Solid

John Macnie - Geometry - 1895 - 388 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....
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Elements of Geometry

Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 556 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 - 562 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....
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Elements of Geometry

Andrew Wheeler Phillips, Irving Fisher - Geometry - 1897 - 376 pages
...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 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,...
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