| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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;... | |
| 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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