 | William Chauvenet - Geometry - 1887 - 336 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 - 414 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 - 420 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 - 340 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 cones whose common altitude... | |
 | 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 are to each other... | |
 | 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... | |
 | John Macnie - Geometry - 1895 - 386 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 - 570 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 - 554 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 - 574 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... | |
| |
Similar cylinders are to each other as the cubes of their altitudes, or as the cubes of the diameters of their bases. 
