 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
 | 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 - 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... | |
 | 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... | |
 | 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... | |
 | Fletcher Durell - 1911 - 234 pages
...V=BXH. (Why?) QED CYLINDERS PROPOSITION V. THEOREM 700. The lateral areas, or the total areas, of two similar cylinders of revolution are to each other...volumes are to each other as the cubes of their radii, of as the cube's of their altitudes. Given two similar cylinders of revolution having their lateral... | |
 | 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,... | |
 | Robert Louis Short, William Harris Elson - Mathematics - 1911 - 216 pages
...From step 2, § oon BC R Then, K R2 K' Or, the areas of two similar polygons are in the same ratio as the squares of their radii, or as the squares of their apothems. THEOREM LXXVIII 284. The area of a regular polygon is equal to one half the product of its... | |
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