| William Chauvenet - 1893 - 340 pages
...COROLLARY I. For a cone of revolution, the proposition may be formulated, V — faR'.If. 30. COROLLARY II. **Similar cones of revolution are to each other as the...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... | |
| 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... | |
| George Clinton Shutts - Geometry - 1894 - 412 pages
...base of the cylinder of revolution. § 381. 584. COROLLARY II. The volumes of similar cylinders oj **revolution are to each other as the cubes of their altitudes, or** the cubes of the radii of their bases. altitude, and radius of the base of one cylinder, and V, H,... | |
| Charles Ambrose Van Velzer, George Clinton Shutts - Geometry - 1894 - 416 pages
...The truth of the theorem may be expressed by the formula CONES. 503. COROLLARY II. The lateral areas **of two similar cones of revolution are to each other as the** squares of their slant heights, or the squares of their altitudes, or the squares of the radii of their... | |
| John Macnie - Geometry - 1895 - 386 pages
...altitude ; then, since B = ir • R1, V = IT . R* . H. 677. COR. 2. The volumes of similar cylinders **of revolution are to each other as the cubes of their altitudes or** radii. For if V and V' be the volumes of two similar cylinders of revolution, B and B' the radii of... | |
| Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 554 pages
...Therelore H. QE 966. COR. I. If the base of the cone is a circle of radius /?, 967. COR. II. The volumes **of two similar cones of revolution are to each other as the cubes of their altitudes, or as** tlic cubes of the radii of their bases. If int. — The method of proof is the same as that followed... | |
| George Albert Wentworth - Geometry - 1896 - 68 pages
...a cone of revolution, and R is the radius of the base, 674. The lateral areas, or the total areas, **of two similar cones of revolution are to each other as the** squares of their altitudes, or of their radii ; and their volumes are to each other as the cubes of... | |
| Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 564 pages
...similar right triangles about homologous sides. 959. COR. III. The lateral areas, or the total areas, **of two similar cones of revolution are to each other as the** squares of their slant heights, or as the squares of their altitudes, or as the squares of the radii... | |
| Andrew Wheeler Phillips, Irving Fisher - Geometry - 1897 - 376 pages
...the volume of a 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 radius of the base. PROPOSITION X. THEOREM. 630. The lateral areas, and also the entire areas, **of two similar cones of revolution are to each other as the** squares of their slant heights, or as the squares of their altitudes, or as the squares of the radii... | |
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