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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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An Elementary Geometry: Plane, Solid and Spherical

William Frothingham Bradbury - Geometry - 1880 - 260 pages
...Circumferences of circles are to each other as their radii, or as their diameters ; and the circles as the squares of their radii, or as the squares of their diameters. For circles are regular polygons of an infinite number of sides (44); and if the circumferences...
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Exercises in Arithmetic

George Albert Wentworth, George Anthony Hill - Arithmetic - 1887 - 448 pages
...sides, or the squares of their radii, or the squares of their apothems. The areas of two circles are as the squares of their radii, or as the squares of their diameters. 323. If a rod 3 ft. high casts a shadow 2 ft. long, how high is a tree which casts a shadow...
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The Elements of Plane and Solid Geometry ...

Edward Albert Bowser - Geometry - 1890 - 414 pages
...equal to the area of four great circles. 791. COR. 2. The areas of the surf/,ct.s of two spheres are to each other as the squares of their radii, or as the squares of their diameters. 792. COR. 3. The area of a zone is iqual to the product of its altitude by the circumference...
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Arithmetic

George Albert Wentworth - Algebra - 1892 - 312 pages
...sides, or the squares of their radii, or the squares of their apothems. The areas of two circles are as the squares of their radii, or as the squares of their diameters. 323. If a rod 3 ft. high casts a shadow 2 ft. long, how high is a tree which casts a shadow...
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The Elements of Solid Geometry: With Numerous Exercises

Arthur Latham Baker - Geometry, Solid - 1893 - 154 pages
...spheres upon which they are situated. COmpare 206. ^ 308. COR. 3. The surfaces of two spheres are to each other as the squares of their radii, or as the squares of their diameters. V ^ 309. COR. 4. The area of a zone is equal to the product of its altitude % the circumference...
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"Wentworth & Hill's Exercise Manual: Arithmetic, Volume 1

George Albert Wentworth - 1894 - 318 pages
...other as the cubes of their radii, or as the cubes of their diameters. The surfaces of two spheres are as the squares of their radii, or as the squares of their diameters. If the heights of two right cylinders, or two right cones, are proportional to the radii...
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Elements of Geometry

George Cunningham Edwards - Geometry - 1895 - 330 pages
...sphere although they are equal. Exercises. — 1. Show that the surfaces of any two spheres are to each other as the squares of their radii, or as the squares of any corresponding lines. 2. Find the surface of a sphere, the diameter of which is one and a half feet....
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Elements of Geometry, Volume 1

Andrew Wheeler Phillips, Irving Fisher - Geometry, Modern - 1896 - 276 pages
...Hint.— Apply 308. 483. COR. II. 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. PROPOSITION V. THEOREM 484. The circumference of a circle is greater than the perimeter of...
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Elements of Geometry

Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 570 pages
...of the sphere. Hence its area is 2irI\.' x 2 A' = 47rA' . 984. COR. V. Two spherical surfaces are to each other as the squares of their radii or as the squares of their diameters. PROPOSITION XI. LEMMA OS3. If a triangle revolve about an axis situated in its plane and...
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An Examination Manual in Plane Geometry

George Albert Wentworth, George Anthony Hill - Geometry - 1896 - 152 pages
...TT.) 268. Theorem. The area of a circle is equal to trt3. 269. Corollary. The areas of circles are to each other as the squares of their radii, or as the squares of their diameters. 270. Theorem. The area of a sector has the same ratio to the area of the circle that the...
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