 The lateral areas, or the total areas, of similar cylinders of revolution are to each other as the squares of their altitudes, or as the squares of their radii ; and their volumes are to each other as the cubes of their altitudes, or as the cubes of their...  Plane and Solid Geometry - Page 312by Arthur Schultze, Frank Louis Sevenoak - 1901 - 370 pagesFull view - About this book
 | William Betz, Harrison Emmett Webb - Geometry, Solid - 1916 - 214 pages
...generated by revolving similar rectangles about homologous sides as axes. PROPOSITION V. THEOREM 887. The lateral areas or the total areas of similar cylinders of revolution are to each other as the squares of their altitudes or as the squares of their radii, and their volumes are to each other as the cubes... | |
 | 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..... | |
 | 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... | |
 | 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; =... | |
 | Fletcher Durell, Elmer Ellsworth Arnold - Geometry, Solid - 1917 - 220 pages
...find the money value of the saving. SOLID GEOMETRY. BOOK VIII PROPOSITION IV. THEOREM 601. The lateral areas of similar cylinders of revolution are to each other as the squares of the altitudes, or as the squares of the radii of the bases. Given two similar cylinders of revolution... | |
 | 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... | |
 | Encyclopedias and dictionaries - 1920 - 934 pages
...revolving round homologous perpendicular sides. The lateral areas, or the total areas, of two similar cones of revolution are to each other as the squares of their radii, or of their slant heights, or of their altitudes, and the volumes of similar cones of revolution are to... | |
 | Herbert Ellsworth Slaught - 1918 - 344 pages
...RATIO OF THE AREAS OF TWO CIRCLES 495. THEOREM VIII. Ttie areas of two circles are in the same ratio as the squares of their radii, or as the squares of their diameters. Proof. Since the area of a circle is Tr?-2, if we have two given circles whose radii are... | |
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