 | George Albert Wentworth - Geometry - 1904 - 496 pages
...COR. 2. The area of a circle is equal to TT times the square of its radius. 464. COR. 3. The areas of two circles are to each other as the squares of their radii. For, if S and S' denote the areas, and R and R' the radii, 465. COR. 4. Similar arcs are to each other... | |
 | 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.... | |
 | 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.... | |
 | Edward Rutledge Robbins - Geometry, Plane - 1906 - 268 pages
...Ex. :t. The diameter of a circle is 25. Find the circumference and area. 447. THEOREM. The areas of two circles are to each other as the squares of their radii, and as the squares of their diameters. To Prove : S : S' = R2 : R'2 = D2 : D'2. And * _ £L?1 - - -... | |
 | Isaac Newton Failor - Geometry - 1906 - 440 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... | |
 | Isaac Newton Failor - Geometry - 1906 - 431 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... | |
 | Edward Rutledge Robbins - Geometry - 1907 - 428 pages
...area. Ex.3. The diameter of a circle is 25. Find the circumference and area. 447. THEOREM. The areas of two circles are to each other as the squares of their radii, and as the squares of their diameters. To Prove: S : S' = .B2: R'2= D2: D'Z. ... S:s'=R2:R'2=tf: D'2... | |
 | Webster Wells - Geometry - 1908 - 336 pages
...respectively. C' p2 D2 ThCn' f = S = f" A3 TT-fl. Jt and §- = te!Lt = VL (§337) That is, the areas of two 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 O, whose area is S, circumference C, and radius... | |
 | Webster Wells - Geometry, Plane - 1908 - 206 pages
...and diameters D and D', respectively. Then, | = "* § = ££ = £• <§337> That is, the areas of two 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 O, whose area is S, circumference C, and radius... | |
 | Webster Wells - Geometry, Plane - 1908 - 208 pages
...diameters D and 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 (7, and... | |
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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. 502. Corollary — When the radius is unity, the area is expressed by ;r. 503. Theorem — The area of a sector is measured by half the product... 
