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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. S TrR2 R* If1' = ~R^ = "cT* = -D'* "
Mensuration of lines, surfaces, and volumes - Page 40
by David Munn - 1873
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Plane Geometry: With Problems and Applications

Herbert Ellsworth Slaught, Nels Johann Lennes - Geometry, Plane - 1918 - 360 pages
...RATIO OF THE AREAS OF TWO CIRCLES 495. THEOREM VIII. The 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 ,rr2, if we have two given circles whose radii are...
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Plane Geometry, with Problems and Application

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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Modern Junior Mathematics, Book 2

Marie Gugle - Mathematics - 1920 - 264 pages
...areas of two circles to find the ratio of their areas? (d) The areas of two circles have the same ratio as the squares of their radii or as the squares of their diameters. Show why radii or diameters may be used in these ratios. 7. (a) The rate of the flow of...
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Solid Geometry

Charles Austin Hobbs - Geometry, Solid - 1921 - 216 pages
...Proposition 298 Theorem The lateral areas, or the total areas, of similar cones of revolution are to each other as the squares of their radii, or as the squares of their altitudes. Ex. 1142. If the slant height of a cone of revolution is equal to the diameter of the base,...
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Drill Book in Plane Geometry

Robert Remington Goff - 1922 - 136 pages
...each other as the squares of any two corresponding sides. *334. Two similar regular polygons are to each other as the squares of their radii, or as the squares of their apothems. *335- The areas of two circles are to each other as the squares of their radii. 337. EXERCISES...
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General Mathematics, Book 2

Raleigh Schorling, William David Reeve - Mathematics - 1922 - 460 pages
...Corollary 2. The area of a circle equals — • • 550. Corollary 3. The areas of two circles are to each other as the squares of their radii or as the squares of their diameters. EXERCISES 1. Draw a graph of the relation A = wr2, and show why the area of a circle is...
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General Mathematics, Book 2

Raleigh Schorling, William David Reeve - Mathematics - 1922 - 476 pages
...other. 536. Corollary. 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. 537. Circumference. The length of a circle in linear units is called the circumference. From...
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Plane Geometry

Walter Burton Ford, Charles Ammermann - Geometry, Modern - 1923 - 406 pages
...Ttr2 is the area of a great circle. 380. Corollary 3. 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. 381. Zones. A zone is a portion of the surface of a sphere bounded by the circumferences...
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Schultze and Sevenoak's Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 484 pages
...to the base, or 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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Essentials of Solid Geometry

David Eugene Smith - Geometry, Solid - 1924 - 256 pages
...product of the diameter and the circumference of a great circle. 2. The areas of two spheres are to each other as the squares of their radii, or as the squares of their diameters. 3. The area of a sphere is 72 sq. in. Find the area of a lune whose angle is 10. It is...
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