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My ALONE po ugdo flavivážimas "Viafya, "toppen wasted throughout a hand, - zu yern Muensta
64
The Jaina Antiquary
[ Vol. XVII
Fig. 13.
An alternative method of finding the volume of a tetrahedron has been given in the demonstration quoted above.
9. The volume of a pyramid is equal to one-third the area of its base multiplied by its height.
Construction: The pyramid can he cut into a number of tetrahedrons. The result follows.
10. The volume of a right cone is equal to one-third the area of its base inultiplied by its height.
Construction: Cut the cone along a radius of the base vertically up to the vertex. Then spread it out so that the base is deformed into a triangle as in 6. The cone is deformed into a tetrahedron of equal volume by virtue of the third principle of deformation. The volume of this tetrahedron is equal to one third the area of the base multiplied by its height, hence the result.
By the fourth principle of deformation the result is true for any cone, right circular or not.
11. The volume of the frustum of a cone could be found out by subtraction, for the frustum is obtained by cutting the cone by a plane parallel to the base. The frustum being given, the original cone by cutting which the frustum has been obtained must be found out. Instead of doing that, the author of the Dhaval finds the volume of the frustum directly taking recourse to construction and the principles of deformation, which we have attempted to recons
truct.
Let a and b be the radii of the base and face of the frustum of a cone whose height is h. Then extracting out a cylinder of radius
