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" The areas of two circles are to each other as the squares of their radii, or as the squares of their diameters. S TrR2 R* If1' = ~R^ = "cT* = -D'* "
Mensuration of lines, surfaces, and volumes - Page 40
by David Munn - 1873
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Syllabus of Geometry

George Albert Wentworth - Mathematics - 1896 - 68 pages
...sphere is equivalent to four great circles. 765. Cor. 2. The areas of the surfaces of two spheres are as the squares of their radii, or as the squares of their diameters. 766. Cor. 3. The area of a zone is equal to the product of its altitude by the circumference...
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Plane Geometry

George D. Pettee - Geometry, Modern - 1896 - 272 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. Dem. —=~ r perim. of sim. reg. are as radii, and areas as sq. of radii C = limit...
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Exercises in Arithmetic

George Albert Wentworth, George Anthony Hill - Arithmetic - 1897 - 476 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...
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Plane and Solid Geometry: Inductive Method

Arthur A. Dodd, B. Thomas Chace - Geometry - 1898 - 468 pages
...the diameter of the sphere? 692. Cor. IV. Show that the areas of the surfaces of two spheres are to each other as the squares of their radii, or as the squares of their diameters. 693. Cor. V. Can you show that the area of a spher694. PROPOSITION XXX. Let the figure represent...
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Plane and Solid Geometry

James Howard Gore - Geometry - 1898 - 232 pages
...equal to the area of four great circles. 534. COR. 2. The areas of the surfaces of two spheres are to each other as the squares of their radii, or as the squares of their diameters. 535. The area of a zone is equal to the product of its altitude by the circumference of...
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The Essentials of Geometry (plane)

Webster Wells - Geometry - 1898 - 284 pages
...73(2 f2 -M Jl y-- That is, <fte areas q/~ two regular polygons of the same number of sides are to each other as the squares of their radii, or as the squares of their apothems. A '\ PROP. VI. THEOREM. *~~^1 350. The area, of a regular polygon is equal to one-half...
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The Essentials of Geometry

Webster Wells - Geometry - 1899 - 180 pages
...For nip is the area of a great O. (?) 673. Cor. V. The areas of the surfaces of two spheres are to each other as the squares of their radii, or as the squares of their diameters. (The proof is left to the pupil ; compare 372.) EXERCISES. 22. Find the area of the surface...
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The Elements of Plane Geometry

Charles Austin Hobbs - Geometry, Plane - 1899 - 266 pages
...Proposition 2OO. Theorem. 237. The areas of two regular polygons of the same number of sides are to each other as the squares of their radii, or as the squares of their apothems. Use a method of proof similar to that used in Prop. 199. Proposition 2O1. Theorem. 238. The...
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Solid Geometry, Volumes 6-9

George Albert Wentworth - Geometry, Solid - 1899 - 248 pages
...the area of the surface of a sphere. 823 825. COR. 2. The areas of the surfaces of two spheres are as the squares of their radii, or as the squares of their diameters. Let R and R' denote the radii, D and I)' the diameters, and *9 and S' the areas of the surfaces...
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Plane and Solid Geometry

George Albert Wentworth - Geometry - 1899 - 496 pages
...total areas, of two similar cones of revolution are to each other as the squares of their altitudes, as the squares of their radii, or as the squares of their slant heights ; and their volumes are to each other as the cubes of their altitudes, as the cubes of...
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