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" A cone, whose slant height is equal to the diameter of its base, is inscribed in a given sphere, and a similar cone is circumscribed about the same sphere. "
Wentworth & Hills's Exercise Manuals: Geometry - Page 33
by George Albert Wentworth - 1889
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Treatise on Geometry and Trigonometry: For Colleges, Schools and Private ...

Eli Todd Tappan - Geometry - 1868 - 438 pages
...one-third the radius of the inscribed sphere. 41. If, about a sphere, a cylinder be circumscribed, also a cone whose slant height is equal to the diameter of its base, then the area and volume of the sphere are two-thirds of the area and volume of the cylinder; and the...
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The Eclectic School Geometry

Evan Wilhelm Evans - Geometry - 1884 - 242 pages
...respectively equivalent to two thirds the surface and volume of the circumscribing cylinder. And if a cone whose slant height is equal to the diameter of its base be circumscribed about the sphere, the surface and volume of the cylinder will be respectively equal...
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Wentworth & Hill's Exercise Manuals: Geometry, Issue 3

George Albert Wentworth - 1884 - 264 pages
...volume of the largest regular four-sided frustum which can be made from it ? 14. The volume of a right cone, whose slant height is equal to the diameter of its base, is V; find the volume of the circumscribed regular triangular pyramid. 15. A cone, whose slant height...
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Exercise Manuals, Issue 3

George Albert Wentworth - 1889 - 276 pages
...volume of the largest regular four-sided frustum which can be made from it? 14. The volume of a right cone, whose slant height is equal to the diameter of its base, is V; find the volume of the circumscribed regular triangular pyramid. 15. A cone, whose slant height...
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Elementary Solid Geometry and Mensuration

Henry Dallas Thompson - Geometry, Solid - 1896 - 226 pages
...1:2:3 (Archimedes's Theorem). 74. If about a sphere a right circular cylinder be circumscribed, also a cone whose slant height is equal to the diameter of its base, then the area and volume of the sphere are two-thirds of the area and volume, respectively, of the...
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Elements of Geometry

George Washington Hull - Geometry - 1897 - 408 pages
...sphere is 10 ft.; find the area of the zone and the volume of the corresponding spherical sector. 472. A cone whose slant height is equal to the diameter of its base is circumscribed about a sphere whose radius is 6 ft.; find the surface and volume of the cone. 478. The...
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Elements of Plane and Solid Geometry

Alan Sanders - Geometry - 1903 - 396 pages
...given radius passing through a given point and tangent to two given planes. 15. A cone of revolution whose slant height is equal to the diameter of its base is circumscribed about a sphere. If the radius of the sphere is a in., what is the volume of the cone...
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Plane and Solid Geometry

Elmer Adelbert Lyman - Geometry - 1908 - 364 pages
...center of the fourth sphere from the level surface, if the radius of the spheres is 1 ft. ? 75. A right cone whose slant height is equal to the diameter of its base is inscribed in a right cylinder whose diameter is the same as that of the cone. Compare the areas and volumes of the...
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Plane and Solid Geometry

William Betz - Geometry - 1916 - 536 pages
...terms of the altitude of the segment and the radius of its base. 8. In a given sphere are inscribed a cone whose slant height is equal to the diameter of its base, and a cylinder whose altitude is equal to the diameter of its base. Prove that the volume of the cylinder...
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Solid Geometry

William Betz, Harrison Emmett Webb - Geometry, Solid - 1916 - 214 pages
...terms of the altitude of the segment and the radius of its base. 8. In a given sphere are inscribed a cone whose slant height is equal to the diameter of its base, and a cylinder whose altitude is equal to the diameter of its base. Prove that the volume of the cylinder...
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