| 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... | |
| 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... | |
| 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... | |
| 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,... | |
| 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,... | |
| 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.... | |
| 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... | |
| 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.... | |
| 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 - = -— = — •... | |
| 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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