 | Education - 1912 - 942 pages
...its altitude. Corollary 2. The total area of a cylinder is equal to the SOLID GEOMETRY SYLLABUS 747 Proposition 15. The lateral areas, or total areas,...transverse sections of a pyramidal space are similar. Corollary I. Parallel transverse sections of a pyramid divide edges and altitude proportionally. Corollary... | |
 | William Chauvenet - 1905 - 336 pages
...the circumference of its base by its altitude. This may be formulated, S = Corollary II. The lateral areas of similar cylinders of revolution are to each other as the squares of their altitudes, or as the squares of the radii of their bases. PROPOSITION III. The volume of a... | |
 | 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... | |
 | 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... | |
 | 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... | |
 | 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... | |
 | 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... | |
 | 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... | |
 | William Herschel Bruce, Claude Carr Cody (Jr.) - Geometry, Modern - 1910 - 284 pages
...to each other as the squares of their radii. M' M 499. COK. 6. The areas of similar segments are to each other as the squares of their radii or as the squares of their chords. For let S and S' denote the areas of the similar As AOB and A'O'B', and K and K' the areas... | |
 | Clara Avis Hart, Daniel D. Feldman - Geometry, Modern - 1911 - 332 pages
...O'A' O'F' (§ 435). 539. Cor. The areas of two regular polygons of the same number of sides are to each other as the squares of their radii or as the squares of their apothems. Ex. 998. Two regular hexagons are inscribed in circles whose radii are 7 inches and 8 inches,... | |
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The lateral areas, or the total areas, of two similar cones of revolution are to each other as the squares of their altitudes... 
