| 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... | |
| 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... | |
| 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 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... | |
| 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... | |
| 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... | |
| 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,... | |
| 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... | |
| 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... | |
| 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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