 | William Chauvenet - Geometry - 1884 - 384 pages
...therefore, RH r'h~ IP h' T t ' R H+R That is, the lateral areas, or the total areas, of similar cylinders oj revolution are to each other as the squares of their altitudes, or as the square* of the radii of their bases. PROPOSITION III.— PROBLEM. 12. The volume of a cylinder is equal... | |
 | William Chauvenet, William Elwood Byerly - Geometry - 1887 - 331 pages
...circumference of its base by its altitude. This may be formulated, Corollary II. The lateral areas of similar cylinders of revolution are to each other...altitudes, or as the squares of the radii of their bases. PROPOSITION III. The volume of a cylinder is equal to the product of its base by its altitude. Corollary... | |
 | William Chauvenet - Geometry - 1888 - 826 pages
...— r H h • R} R H+R T t " That is, the lateral areas, or the total areas, of similar cylinders oj revolution are to each other as the squares of their...altitudes, or as the squares of the radii of their bases. PROPOSITION III.— PROBLEM. 12. The volume of a cylinder is equal to the product of its base by its... | |
 | Edward Albert Bowser - Geometry - 1890 - 418 pages
...and .. . T' ~ R'(R' + H') ._ JP __R' ' "" H" ~R"- ( ' R' R' + H' Therefore, the lateral areas, or the total areas, of two similar cylinders of revolution...altitudes, or as the squares of the radii of their bases. EXERCISES. 1. Required the lateral area, and also the total area, of a cylinder of revolution whose... | |
 | Edward Albert Bowser - Geometry - 1890 - 420 pages
...height of the complete cone : find the ratio of the volume of the frustum to that of the cone. 48. The total areas of two similar cylinders of revolution are to each other as 25 : 49 : find the ratio of their volumes. 49. The altitude of a cone of revolution is 10, and its... | |
 | George Albert Wentworth - Geometry - 1888 - 466 pages
...is irR2, and F= itR2 X H. PROPOSITION XXXIV. THEOREM. 651. The lateral areas, or the total areas, of similar cylinders 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 their altitudes, or of their radii.... | |
 | William Chauvenet - 1893 - 340 pages
...circumference of its base by its altitude. This may be formulated, S = ZvRH. Corollary II. The lateral areas of similar cylinders of revolution are to each other...altitudes, or as the squares of the radii of their bases. PROPOSITION III. The volume of a cylinder is equal to the product of its base by its altitude. Corollary... | |
 | William C. Bartol - Geometry, Solid - 1893 - 106 pages
...lateral surfaces are to each other as the perimeters of the bases. EXERCISES. 98. THEOREM. The volumes of two similar cylinders of revolution are to each other as the cube^ of their altitudes, or as the cubes of the radii of their bases. 99. THEOREM. The surfaces, lateral... | |
 | Charles Ambrose Van Velzer, George Clinton Shutts - Geometry - 1894 - 522 pages
...and R the radius of the base of the cylinder of revolution. 483. COROLLARY II. The lateral areas of similar cylinders of revolution are to each other...altitudes or as the squares of the radii of their bases. I«et A, H and R repre sent respectively the area, altitude, and radius of the base of one cylinder... | |
 | George Clinton Shutts - Geometry - 1894 - 412 pages
...base of the cylinder of revolution. 305 581. COROLLARY II. The lateral areas of similar cylinders 0} revolution are to each other as the squares of their...altitudes, or as the squares of the radii of their bases. Let A, H, and R represent, respectively, the area, altitude, and the radius of the base of one cylinder,... | |
| |
The lateral or total areas of two similar cones of revolution are to each other as the squares of their slant heights... 
