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" Similar cylinders are to each other as the cubes of their altitudes, or as the cubes of the diameters of their bases. "
The Elements of Solid Geometry - Page 46
by William C. Bartol - 1893 - 95 pages
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Solid Geometry, Volumes 6-9

George Albert Wentworth - Geometry, Solid - 1899 - 248 pages
...the base, B = irR\ • 463 PROPOSITION XLI. THEOREM. 726. The lateral areas, or the total areas, of two similar cones of revolution are to each other as the square* of their altitudes, as the squares of their radii, or as the squares of their slant heights...
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Manual of Examinations for the ...

Civil service - 1899 - 134 pages
...MECHANICS. 6. Assuming the formula for determining the solidity of a cone as proved, show that the volumes of two similar cones of revolution are to each other as the cuhes of their heights. 7. Given two adjacent sides, a and h, of a triangle, and also the included...
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The Essentials of Geometry

Webster Wells - Geometry - 1899 - 178 pages
...and R the radius of the base, of a circular cone, PROP. VI. THEOREM. 656. TJie lateral or total areas of two similar cones of revolution are to each other as the squares of their slant heights, or as the squares of their altitudes, or as the squares of the radii...
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Elementary Geometry, Plane and Solid: For Use in High Schools and Academies

Thomas Franklin Holgate - Geometry - 1901 - 462 pages
...homologous sides. 6. Show that the volumes of two similar right circular cones are in the same ratio as the cubes of their altitudes, or as the cubes of the radii of their bases. 8. Show that the lateral area of the frustum of a right circular cone is equal to the sum of the circumferences...
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Plane and Solid Geometry

Arthur Schultze - 1901 - 392 pages
...height is 13. SOLID GEOMETRY PROPOSITION XXXIII. THEOREM 666. The lateral areas, or the total areas, of two similar cones of revolution are to each other as the squares of their altitudes, as the squares of their radii, or as the squares of their slant heights...
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Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1902 - 394 pages
...height is 13. SOLID GEOMETRY PROPOSITION XXXIII. THEOREM 666. '77ie lateral areas, or the total areas, of two similar cones of revolution are to each other as the squares of their altitudes, as the squares of their radii, or as the squares of their slant heights...
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Solid Geometry, Volumes 6-9

George Albert Wentworth - Geometry, Solid - 1902 - 248 pages
...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 radii. Let S, S' denote the lateral areas, T, T' the total areas, V, V the volumes, H, H' the...
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Manual of Examinations for the ...

Civil service - 1902 - 180 pages
...MECHANICS. 6. Assuming the formula for determining the solidity of a cone as proved, show that the volumes of two similar cones of revolution are to each other as the cubes of their heights. 7. Given two adjacent sides, a and b, of a triangle, und also the included angle...
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Solid Geometry, Volumes 6-9

George Albert Wentworth - Geometry, Solid - 1902 - 246 pages
...the base, QED B = -rrR*. 463 PROPOSITION XLI. THEOREM. 726. The lateral areas, or the total areas, of two similar cones of revolution are to each other as the squares of their altitudes, as the squares of their radii, or as the squares of their slant heights;...
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Elements of Plane and Solid Geometry

Alan Sanders - Geometry - 1903 - 392 pages
...revolved about homologous legs as axes. PROPOSITION XIV. THEOREM 1046. The lateral or entire areas of two similar cones of revolution are to each other as the squares of their altitudes or as the squares of the radii of their bases; and their volumes are to...
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