 | Edward Olney - Geometry - 1883 - 352 pages
...Whence, by substitution, we have H* PROPOSITION XVIII. 606. Theorem.—The volumes of similar cylinders of revolution are to each other as the cubes of their...altitudes, or as the cubes of the radii of their bases. DEMONSTRATION. For, by (595), V = v and v = irhr*. 1 nce ' 7" ~ ~rfvr• ~ ~W ' V _ irHR' _ HR' and,... | |
 | Edward Olney - Geometry - 1883 - 352 pages
...iff _ A _ H IJT - a - T( . ED PROPOSITION XII. 641. Theorem. — The volumes of similar cones are to each other as the cubes of their altitudes, or as the cubes of the radii of their bases. SYNOPSIS OF DEMONSTRATION. Let R and r be the radii of their bases, and /land h their altitudes. Tfi... | |
 | Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...themselves are to each other as the cubes of their homologous edges. Cor. 2. Similar prisms are to each other as the cubes of their altitudes, or as the cubes of any other homologous lines. PROPOSITION XX. THEOREM. Similar pyramids are to each other as the cubes... | |
 | Webster Wells - Geometry - 1886 - 392 pages
...altitudes, or as the squares of the radii of their bases; and their volumes are to each other as tlie cubes of their altitudes, or as the cubes of the radii of their . J*.. J3. jrustum of a circular cone is equivalent to the sum f three cones, having for their common... | |
 | William Chauvenet, William Elwood Byerly - Geometry - 1887 - 331 pages
...its altitude. Corollary I. For a cone of revolution this proposition may be formulated, Corollary II. Similar cones of revolution are to each other as the...their altitudes, or as the cubes of the radii of their PBOPOSITION VIII. The area of the surface generated by a straight line revolving about an axis in its... | |
 | William Chauvenet, William Elwood Byerly - Geometry - 1887 - 342 pages
...revolution, the proposition may be formulated, V = Jrr.K ! . H. 30. COROLLARY II. Similar cones of -so 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 Chauvenet - Geometry - 1887 - 336 pages
...Proposition IX., CoroM lary.) 13. COROLLARY II. The volumes of similar cylinders of revoJ lution are to each other as the cubes of their altitudes, or as the cubes of their radii. THE CONE. 14. Definition. The area of the convex, or lateral, surface of a cone is called... | |
 | Edward Albert Bowser - Geometry - 1890 - 414 pages
...revolution, whose altitude is H and 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...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
...2. By the process that was employed in (756) we may show that the lateral areas, or the total areas, of two similar cones of revolution are to each other as the squares of their radii, or of their slant heights, or of their altitudes. Proposition 6. Theorem. 776.... | |
 | Edward Albert Bowser - Geometry - 1891 - 424 pages
...is R, we have V = ^7rR•H. (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 bases. (759) EXERCISES. 1. Required the lateral area and volume of a right circular cone whose altitude is... | |
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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. 
