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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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Plane Geometry

Claude Irwin Palmer, Daniel Pomeroy Taylor - Geometry, Plane - 1915 - 320 pages
...equal to \ird?. r = \d and c = ird. 495 500. Theorem. The areas of two circles are in the same ratio as the squares of their radii or as the squares of their diameters. Proof. Let A and A', r and r', and d and d' denote the area?, radii, and diameters respectively...
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Plane Geometry

Webster Wells, Walter Wilson Hart - Geometry, Plane - 1915 - 330 pages
...diameter 10 ? 387. Cor. The areas of two regular polygons of the same number of sides have the same ratio as the squares of their radii or as the squares of their apothems. 1. Let K and K' represent the areas of the polygons AC and A'C' respectively. Then - = -....
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Plane Geometry

John Charles Stone, James Franklin Millis - Geometry - 1916 - 306 pages
...equals irJR?. For A = J RC= i R x 2 -rrR = 7T.B2. 282. Corollary 2. — The areas of two circles are to each other as the squares of their radii, or as the squares of their diameters. For ^ = a Trr2 r2 d2 283. A sector of a circle. — The figure formed by an arc of a circle...
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Solid Geometry

John H. Williams, Kenneth P. Williams - Geometry, Solid - 1916 - 184 pages
...~ForS = AEX2irR = 2RX2irR = 4:irR : >=7rD 2 . 409 721. COR. 2. The surfaces of two spheres are to each other as the squares of their radii or as the squares of their diameters. For S 722. A zone is the portion of the surface of a sphere included between parallel planes.....
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Plane and Solid Geometry

William Betz - Geometry - 1916 - 536 pages
...circumference and its radius. That is, S = RC. But C = 2 irR. 466. The areas of two circles are to each other as the squares of their radii, or as the squares of their diameters. S _ irR* _ R'2 _ D2 S'~ For •n-R1' R1' 467. A sector of a circle is the figure formed...
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Solid Geometry

William Betz, Harrison Emmett Webb - Geometry, Solid - 1916 - 214 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 radii, as the cubes of their...
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Plane and Solid Geometry

Webster Wells, Walter Wilson Hart - Geometry - 1916 - 490 pages
...diameter 10 ? 387. Cor. The areas of two regular polygons of the same number of sides have the same ratio as the squares of their radii or as the squares of their apothems. 1. Let K and K' represent the areas of the polygons AC and A'C' respectively. Then -f; =...
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Plane and Solid Geometry

Claude Irwin Palmer, Daniel Pomeroy Taylor - Geometry - 1918 - 460 pages
...formula for the area of a sphere are S=2irrd, and S=ird-. 805. Theorem. The areas of two spheres are to each other as the squares of their radii; or, as the squares -of their diameters. For, if S, and S' are the areas of two spheres, S 4irr~ r2 . S ird~ d? , S' 4 7ir'2 r'2>...
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Solid Geometry

Claude Irwin Palmer - Geometry, Solid - 1918 - 192 pages
...formula for the area of a sphere are S=2irrd, and S=ird?. 805. Theorem. The areas of two spheres are to each other as the squares of their radii; or, as the squares of their diameters. For, if S, and S' are the areas of two spheres, S 47rr2 ^ r2 S ^ Trd2 ^ d2 396 SOLID GEOMETRY...
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Schultze and Sevenoak's Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1918 - 486 pages
...But (277) QED 683. COR. 2. Sections made by planes parallel to the bases of a circular cone are to each other as the squares of their radii, or as the squares of their distances from the vertex of the cone. PROPOSITION XXX. THEOREM 684. The lateral area of a cone of...
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