| 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... | |
| 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 - = -.... | |
| 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... | |
| 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..... | |
| William Betz - Geometry - 1916 - 536 pages
...circumference and its radius. That is, S = ħRC. 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... | |
| 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... | |
| 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; =... | |
| 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>... | |
| 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... | |
| 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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