 | William James Milne - Arithmetic - 1877 - 418 pages
...contents of a sphere. A sphere may be regarded as composed of pyramids whose kases form the surface of the sphere, and whose altitude is the radius of the sphere. Hence the following is the RULE.—1. Multiply the convex surface by one-third of the radius; or, 2.... | |
 | William Henry Harrison Phillips - Geometry - 1878 - 236 pages
...number of infinitely small pyramids, whose vertices are at the centre, whose bases form the surface of the sphere, and whose altitude is the radius of the sphere. The volume of these pyramids is equal to one-third the sum of their bases multiplied by their altitude... | |
 | William James Milne - Arithmetic - 1892 - 440 pages
...contents of a sphere. • A sphere may be regarded as composed of pyramids whose bases form the surface of the sphere, and whose altitude is the radius of the sphere. Hence the following rule : RULE. — 1. Multiply the convex surface by one third of the radius; or,... | |
 | Archimedes - Geometry - 1897 - 532 pages
...with Prop. 26. COR. The solid circumscribed about the smaller sphere is greater than four times the cone whose base is a great circle of the sphere and whose heigJit is equal to the radius of the sphere. For, since the surface of the solid is greater than four... | |
 | Mathematics - 1898 - 228 pages
...1, the other on a sphere of radius 2. 8. Compare the volume of a sphere whose radius is R with that of a cone whose base is a great circle of the sphere and whose altitude is R. JUNE 1889. PLANE. 1. Every point in the bisector of an angle is equally distant from the sides of... | |
 | Yale University - 1898 - 212 pages
...i, the other on a sphere of radius 2. 8. Compare the volume of a sphere whose radius is R with that of a cone whose base is a great circle of the sphere and whose altitude is R. JUNK 1889. P 1. Every point in the bisector of an angle is equally distant from the sides of the... | |
 | Jacob Henry Minick, Clement Carrington Gaines - Business mathematics - 1904 - 412 pages
...A sphere may be regarded as composed of an infinite number of pyramids whose bases form the surface of the sphere and whose altitude is the radius of the sphere. Hence, RULE. — Multiply the convex surface T)y one-third of the radius / or, multiply the cube of... | |
 | George E. Mercer - Arithmetic - 1909 - 312 pages
...sq. cm ? A sphere may be regarded as composed of pyramids whose bases taken together form the surface of the sphere, and whose altitude is the radius of the sphere. Since the volume of a pyramid is the product of the base and J of the altitude, the volume of a sphere... | |
 | George E. Mercer, Mabel Bonsall - Arithmetic - 1914 - 324 pages
...sq. cm ? A sphere may be regarded as composed of pyramids whose bases taken together form the surface of the sphere, and whose altitude is the radius of the sphere. Since the volume of a pyramid is the product of the base and ^ of the altitude, the volume of a sphere... | |
 | Asger Aaboe - History - 1963 - 154 pages
...5, its volume is multiplied by (£)3. Thus sphere = 4- cone CAD, or a sphere is equd to four times a cone -whose base is a great circle of the sphere and whose height is the sphere's radius. It is now a simple matter to show that a sphere is two-thirds of its... | |
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... solid is, as before, a solid inscribed in a larger sphere ; and, since the perpendicular on any side of the revolving polygon is equal to the radius of the inner sphere, the proposition is identical with Prop. 26. COR The solid circumscribed about... 
