Journals Proceedings

Abstract

Solids of revolution have applications in various fields such as manufacturing (casting, machining), computer aided designing etc., wherein axis-symmetric solids are generated by revolution of curves. Most often the curves corresponding to these solids are irregularly shaped. Thus, regular integration cannot be applied to obtain definite volume of such solids. Hence, given a set of function values (radii), an approximation of volume of the solid can be made. The approximation introduced here (frustum approximation), divides the solid into a number of frustums of cones, instead of following the conventional approach of dividing the solid into cylinders. The summation of all the individual volumes of the frustums, gives the approximate volume of the total solid. The study also compares and analyzes the frustum approximation with existing methods of approximating integrals. The results indicate that for all sub-intervals of solids that are ‘concave’ in nature, the frustum approach generates a better approximation compared to existing methods.