 S7rR = 4WR1. (789) Therefore, the area of the surface of a sphere is equal to the area of four great circles. 791. COR. 2. TJie areas of the surfaces of two spheres are to each other as the squares of their radii, or as the squares of their diameters.  Plane and Solid Geometry: Inductive Method - Page 376by Arthur A. Dodd, B. Thomas Chace - 1898 - 406 pagesFull view - About this book
 | Benjamin Greenleaf - Geometry - 1873 - 202 pages
...by D, its surface will be represented by 4 * X .«2, or - X #2. 366. Cor. 5. Hence, the surfaces of spheres are to each other as the squares of their radii or diameters. 367. Cor. 6. If the altitude of a zone or segment is represented by H, the surface of a... | |
 | Benjamin Greenleaf - Geometry - 1874 - 206 pages
...diameter by D, its surface will be represented by 4 * XR*, or = X D"-. 366. Cor. 5. Hence, the surfaces of spheres are to each other as the squares of their radii or diameters. 367. Cor. 6. If the altitude of a zone or segment is represented by H, the surface of a... | |
 | William Chauvenet - Geometry - 1875 - 390 pages
...surfaces of two spheres whose radii are R and R ' ; then, S ^ 4xR' _ (2.R)2 _IP_t ~ ~ ~ R"' hence, the surfaces of two spheres are to each other as the squares of their diameters, or as the squares of their radii. PROPOSITION XII— LEMMA. 44. If a triangle revolves... | |
 | William Guy Peck - Conic sections - 1876 - 376 pages
...will be equal to 2jrR x 2R, or to 4jtR s , that is, to four great circles. Cor. 2. The surface of any two spheres are to each other as the squares of their radii. Cor. 3. The area of any zone is equal to the circumference of a great circle multiplied by its altitude.... | |
 | William Frothingham Bradbury - Geometry - 1877 - 262 pages
...Circumferences of circles are to each other as their radii, or as their diameters ; and the circles as the squares of their radii, or as the squares of their diameters. For circles are regular polygons of an infinite number of sides (44) ; and if the circumferences of... | |
 | William Henry Harrison Phillips - Geometry - 1878 - 236 pages
...equal to four times the area of one of its great circles. BOOK VIII.] MEASUREMENT OF SOLIDS. COR. 3. The surfaces of two spheres are to each other as the squares of their radii. COR. 4. If a right cylinder be circumscribed about a sphere whose radius is R, then R = radius of its... | |
 | William Frothingham Bradbury - Geometry - 1880 - 260 pages
...Circumferences of circles are to each other as their radii, or as their diameters ; and the circles as the squares of their radii, or as the squares of their diameters. For circles are regular polygons of an infinite number of sides (44); and if the circumferences of... | |
 | Charles Scott Venable - 1881 - 380 pages
...the sphere is equal to^ the area of the circle whose radius is the diameter of the sphere. COR. 3. The surfaces of two spheres are to each other as the squares of their radii or the squares of their diameters, or as the squares of the circumferences of their great circles. For,... | |
 | Joseph Anthony Gillet - Astronomy - 1882 - 496 pages
...distance through its centre. The radius of a sphere is the distance from the surface to the centre. The surfaces of two spheres are to each other as the squares of their radii or diameters ; and the volumes of two spheres are to each other as the cubes of their radii or diameters.... | |
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