 | George Albert Wentworth - Algebra - 1892 - 312 pages
...the dome, at 60 cents per foot. Two cubes are to each other (in volume) as the cubes of their edges. Two spheres are to each other as the cubes of their radii, or as the cubes of their diameters. The surfaces of two spheres are as the squares of their radii, or as the squares of their diameters.... | |
 | William Chauvenet - 1893 - 340 pages
...42. COROLLARY I. The result of this proposition may be formulated, 43. COROLLARY II. The volumes of two spheres are to each other as the cubes of their radii, or as the cubes of their diameters. PROPOSITION XII.—THEOREM. 44. The volume of a spherical sector is equal to the area of the zone which... | |
 | Arthur Latham Baker - Geometry, Solid - 1893 - 154 pages
...J tr • (2 r) 3 . For Sph. S = 4irr*, .: Sph. V=i• rSph. S=$'irr*. 332. Colt. /t. The volumes of two spheres are to each other as the cubes of their radii. Compare § 200. PROPOSITION XXIT. THEOREM. "i"' 334. The volume of a apherif.al segment is equal to... | |
 | William C. Bartol - Geometry, Solid - 1893 - 106 pages
...being the diameter. For, V = iE•S. and S = 4 n E2; hence V = J n E3 or £ n D3. 200. COROLLARY 2. Spheres are to each other as the cubes of their radii or diameters. For, Y fTrE3 E3 -, V i^rD3 D3 ' __ 3 . o -r\ n — " ___ V"' ~ I- n E/3 ~ E73 ' ' Y7 ~"... | |
 | George Albert Wentworth - 1894 - 318 pages
...the dome, at 60 cents per foot. Two cubes are to each other (in volume) as the cubes of their edges. Two spheres are to each other as the cubes of their radii, or as the cubes of their diameters. The surfaces of two spheres are as the squares of their radii, or as the squares of their diameters.... | |
 | Webster Wells - Geometry - 1894 - 400 pages
...of two spheres, R and R' their radii, and D and // their diameters. Then, That is, £/ie volumes of two spheres are to each other as the cubes of their radii, or as the cubes of t/teir diameters. 692. COR. III. Let OAB be a sector ijf a circle. It may be proved, as in § 689,... | |
 | George Cunningham Edwards - Geometry - 1895 - 328 pages
...Apply the prismoidal formula to a sphere. 2. Apply the prismoidal formula to a hemisphere. 3. Show that the volumes of any two spheres are to each other as the cubes of their radii, or as the cubes of any corresponding lines. 4. The circumference of a great circle of a sphere being 6 ft., find the volume.... | |
 | John Macnie - Geometry - 1895 - 390 pages
...altitude has for limit R, 348 708. COR. 1. Since S = .iir.B'i. (700) V=1SX • 709. COE. 2. The volumes of spheres are to each other as the cubes of their radii or diameters. For since V= fir • R" = J TT//, and V' = ^irB'3 = £ TT • a'3, F: V' = If' : R'3 = If... | |
 | Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 344 pages
...areas of the surfaces of two spheres are to each other as the squares of their radii. 2. The volumes of two spheres are to each other as the cubes of their radii. Theorem 29. Two right circular cylinders are similar if their elements have the same ratio as the radii... | |
 | Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 346 pages
...areas of the surfaces of two spheres are to each other as the squares of their radii. 2. The volumes of two spheres are to each other as the cubes of their radii. Theorem 29. Two right circular cylinders are similar If their elements have the same ratio as the radii... | |
| |
The volumes of two spheres are to each other as the cubes of their radii, or as the cubes of their diameters. 
