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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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Solid Geometry

Fletcher Durell - Geometry, Solid - 1904 - 232 pages
...PROPOSITION X. THEOREM 724. The lateral areas, or the total areas, of two similar cones of revolution are to each other as the squares of their radii, or as the squares of their altitudes, or as the squares of their slant heights; and their volumes are to each other as the cubes...
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Plane and Solid Geometry

George Albert Wentworth - Geometry - 1904 - 496 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 D' the diameters, and S and S' the areas of the surfaces...
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School Science and Mathematics, Volume 12

Education - 1912 - 942 pages
...SYLLABUS 747 Proposition 15. The lateral areas, or total areas, of similar cylinders of revolution are to each other as the squares of their radii, or as the squares of their altitudes. Definition. Pyramidal surface. Pyramidal space. Edges. Faces. Vertex. Transverse section....
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School Science and Mathematics, Volume 12

Education - 1912 - 914 pages
...revolution. Proposition 15. The lateral areas, or total areas, of similar cylinders of revolution are to each other as the squares of their radii, or as the squares of their altitudes. Definition. Pyramidal surface. Pyramidal space. Edges. Faces. Vertex. Transverse section....
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Plane and Solid Geometry

Isaac Newton Failor - Geometry - 1906 - 431 pages
...AD x 2 TrE = 2 E x 2 TrE = 4 TrE2. 831 COROLLARY 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. 832 COROLLARY 3. The area of a zone is equal to the product of its altitude by the circumference...
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Plane and Solid Geometry

Isaac Newton Failor - Geometry - 1906 - 440 pages
...circle is irB2. PROOF. S = iRxC = £Rx2TrR = TrR2. 465 COROLLARY 2. The areas of two circles are to each other as the squares of their radii, or as the squares of their diameters. PROOF. S:S' = irR2:irRB = R1:R"=DI:D'2. 466 COROLLARY 3. The area of a sector is equal to...
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Plane and Solid Geometry

Edward Rutledge Robbins - Geometry - 1907 - 428 pages
...cones of revolution : I. The lateral areas are to each other as the squares of their altitudes, or as the squares of their radii, or as the squares of their slant heights. II. The total areas are to each other as the squares of their altitudes, or as the squares...
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New Plane and Solid Geometry

Webster Wells - Geometry - 1908 - 336 pages
...a sphere is equivalent to four great circles. 593. 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 § 338.) Ex. 25. Find the area of the surface...
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New Plane Geometry

Webster Wells - Geometry, Plane - 1908 - 208 pages
...D', respectively. Then, 8 ^ R2 and 2-t = t*"^ = ^- (§ 337) That is, the areas oftwo circles are to each other as the squares of their radii, or as the squares of their diameters. 339. Let s be the area, and c the arc, of a sector -of a 0, whose area is S, circumference...
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Plane and Solid Geometry

Elmer Adelbert Lyman - Geometry - 1908 - 364 pages
...of the zone generated by the arc CD = GO x 2irR. 711. Corollary 2. The areas of two spheres are to each other as the squares of their radii, or as the squares of their diameters. SUGGESTION. Let R and R' be the radii of two spheres, then 47rR2 and 4xR'J will be their...
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