 | Thomas Lund - Geometry - 1854 - 520 pages
...The inner diameter of a foot-ball is 6 in. ; how many cubic inches of air does it contain? 295. Given that the volume of a cone is equal to onethird of the cylinder with the same base and height, prove that the volume of a sphere is two-thirds of the circumscribing... | |
 | Eli Todd Tappan - Geometry, Modern - 1864 - 288 pages
...circumference of the base by the sum of the slant hight and the radius of the base (499). 725. Corollary. — The volume of a cone is equal to one-third of the product of the base by the altitude. 72G. The frustum of a cone is defined in the same way as the frustum of a pyramid.... | |
 | Eli Todd Tappan - Geometry - 1868 - 432 pages
...circumference of the base by the sum of the slant higlit and the radius of the base (499). 725. Corollary — The volume of a cone is equal to one-third of the product of the base by the altitude. 726. The frustum of a cone is defined in the same way as the frustum of a pyramid.... | |
 | Eli Todd Tappan - Geometry - 1873 - 288 pages
...circumference of the base by the sum of the slant hight and the radius of the base (499). 725. Corollary — The volume of a cone is equal to one-third of the product of the base by the altitude. 726. The frustum of a cone is defined in the same way as the frustum of a pyramid.... | |
 | Henry Lewis (M.A.) - Measurement - 1875 - 104 pages
...polygon (p. 29), so the cone is only a species of pyramid, and may be treated in exactly the same way. The volume of a cone is equal to one-third of the product of the area of its base and its altitude. In other words the volume of a cone is exactly equal to onethird of the volume of... | |
 | Catherinus Putnam Buckingham - Calculus - 1875 - 362 pages
...the origin we have V=o, x=o, and hence C=o, and making x=h we have for the entire cone • that is, the volume of a cone is equal to one-third of the product of its base by its altitude, or equal to one-third of a cylinder of the same base and altitude. (247)... | |
 | Catherinus Putnam Buckingham - Calculus - 1875 - 374 pages
...origin we have V=o, x=o, and hence C=o, and making x=h we have for the entire cone V=«*'3 that is, the volume of a cone is equal to one-third of the product of its base by its altitude, or equal to one-third of a cylinder of the same base and altitude. (247)... | |
 | Aaron Schuyler - Geometry - 1876 - 384 pages
...of the pyramid, 62 : &, :: a'2 : a2; .-. b' : b : : a'« : a'. (?) 442. Proposition IX.— Theorem. The volume of a cone is equal to one-third of the product of its base by its altitude. Let C denote the volume of the cone V-AC; b, its base ; a, its altitude ;... | |
 | Benjamin Williamson - Calculus - 1877 - 372 pages
...one-third of its height.* * This demonstration is taken from Clairaut's " Elcmens de Geometric." Thu student is supposed familiar with the more ancient...equal to one-third of the product of the area of its bane into its height. If the base of a pyramid be a regular polygon, and the vertex be equidistant... | |
 | Benjamin Williamson - Calculus of variations - 1880 - 398 pages
...follows that the volume of any pyramid is the area of its base multiplied by one-third of its height.* If the base of the pyramid be any closed curve, the...a cone ; and we infer that the volume of a •cone u equal to one-third of the product of the area of its base into its height. If the base of a pyramid... | |
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The volume of a cone is equal to one-third of the product of the base by the altitude. 
