 The lateral or total areas of two similar cglinders of revolution are to each other as the squares of their altitudes, or as the squares of the radii of their bases ; and their volumes are to each, other as the cubes of their altitudes, or as the cubes...  The Elements of Solid Geometry - Page 30by William C. Bartol - 1893 - 95 pagesFull view - About this book
 | 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,... | |
 | John Macnie - Geometry - 1895 - 386 pages
...about homologous arms as axes. 687. COB. 2. The lateral areas, or the total areas, of similar cones of revolution, are to each other as the squares of their altitudes, or as the squares of their radii. This may be proved as was Cor. 3 of Prop. I. 688. DEFINITION. A truncated cone is the... | |
 | George Albert Wentworth - Mathematics - 1896 - 68 pages
...revolution, then the area of the base is -n-E2, and V=irli2H. 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.... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 570 pages
...altitude, R the radius, and V the volume of a circular cylinder. Then V=-nR"H. 942. 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 TrA"2// /?* H ff3 H //3 A'3 OUTLINE PROOF:... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 574 pages
...of similar rectangles about homologous sides. 939. COR. III. The lateral areas, or the total areas, of two similar cylinders of revolution are to each...the squares of their altitudes, or as the squares of their radii. S 2irRH RHHHH* R1 OUTLINE PROOF : - = = — x — = — x — =-— = —. s zvrh rhhh... | |
 | George Washington Hull - Geometry - 1897 - 408 pages
...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 of their bases; and their volumes are to each other as the cubes of their slant heights, or as the cubes of their altitudes,... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1897 - 376 pages
...altitude, £ the radius, and V 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 :... | |
 | Webster Wells - Geometry - 1899 - 196 pages
...III. THEOREM. 646. The lateral or total areas of two similar cylinders of revolution (§ 550) are to each other as the squares of their altitudes, or as the squares of the radii of their bases ; and their volumes are to each other as the cubes of their altitudes, or as the cubes of the radii... | |
 | Webster Wells - Geometry - 1899 - 424 pages
...III. THEOREM. 646. The lateral or total areas of two similar cylinders of revolution (§ 550) are to each other as the squares of their altitudes, or as the squares of the radii of their bases ; and their volumes are to each other as the cubes of their altitudes, or as the cubes of the radii... | |
 | William James Milne - Geometry - 1899 - 396 pages
...their bases? Theorem. The lateral areas, or the total areas, of similar cones of recolution are to each other as the squares of their altitudes, or as the squares of the radii of their bases. Data : Any two similar cones of revolution, whose altitudes are H and H', slant heights L and L', and... | |
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