 The lateral areas, or the total areas, of similar cylinders of revolution are to each other as the squares of their altitudes, or as the squares of their radii ; and their volumes are to each other as the cubes of their altitudes, or as the cubes of their...  Plane and Solid Geometry - Page 312by Arthur Schultze, Frank Louis Sevenoak - 1901 - 370 pagesFull view - About this book
 | Edward Albert Bowser - Geometry - 1890 - 414 pages
...equal to the area of four great circles. 791. COR. 2. The areas of the surf/,ct.s of two spheres are to each other as the squares of their radii, or as the squares of their diameters. 792. COR. 3. The area of a zone is iqual to the product of its altitude by the circumference... | |
 | Edward Albert Bowser - Geometry - 1890 - 420 pages
...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. The lateral area of /z... | |
 | George Albert Wentworth - Geometry - 1888 - 466 pages
...of revolution, then the area of the base 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,... | |
 | George Albert Wentworth - Geometry - 1892 - 468 pages
...the number of the lateral faces, V'=B'xH. .-.V = BxII §260 QED PROPOSITION XXXIV. THEOREM. 651. Tlte lateral areas, or the total areas, of similar cylinders of revolution are to each other as tha squares of their altitudes, or of their radii ; and their volumes are to each other as the cubes... | |
 | George Albert Wentworth - Algebra - 1892 - 312 pages
...sides, or the squares of their radii, or the squares of their apothems. The areas of two circles are as the squares of their radii, or as the squares of their diameters. 323. If a rod 3 ft. high casts a shadow 2 ft. long, how high is a tree which casts a shadow... | |
 | Arthur Latham Baker - Geometry, Solid - 1893 - 154 pages
...spheres upon which they are situated. COmpare § 206. ^ 308. COR. 3. The surfaces of two spheres are to each other as the squares of their radii, or as the squares of their diameters. V ^ 309. COR. 4. The area of a zone is equal to the product of its altitude % the circumference... | |
 | William Chauvenet - 1893 - 340 pages
...may be formulated, if E is the radius of the base and H the altitude. 10. COROLLARY II. The lateral areas of similar cylinders of revolution are to each other as the squares of their altitudes, or as the squares of the radii of their bases. Suggestion. = "' s EE If H' . EH... | |
 | Charles Ambrose Van Velzer, George Clinton Shutts - Geometry - 1894 - 522 pages
...altitude, 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 as the squares of their altitudes or as the squares of the radii of their bases. I«et A, H and R repre sent respectively... | |
 | George Albert Wentworth - 1894 - 318 pages
...other as the cubes of their radii, or as the cubes of their diameters. The surfaces of two spheres are as the squares of their radii, or as the squares of their diameters. If the heights of two right cylinders, or two right cones, are proportional to the radii... | |
 | George Albert Wentworth - Geometry - 1895 - 468 pages
...§260 a to. SOLID GEOMETRY. — BOOK VII. PROPOSITION XXXIV. THEOREM. 651. The lateral areas, or tJie 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,... | |
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