 | 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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Similar cylinders are to each other as the cubes of their altitudes, or as the cubes of the diameters of their bases. 
