旋转体体积计算方法的探讨  

Discussion on Calculation Method of Volume of Revolution

作　　者：孟献青 MENG Xian-qing(School of Mathematics and Statistics,Shanxi Datong University,Datong Shanxi,037009;Institute of Quantum Information Science,Shanxi Datong University,Datong Shanxi,037009)

机构地区：[1]山西大同大学数学与统计学院,山西大同037009 [2]山西大同大学量子信息科学研究所,山西大同037009

出　　处：《山西大同大学学报（自然科学版）》2022年第4期27-29,共3页Journal of Shanxi Datong University(Natural Science Edition)

基　　金：山西大同大学教学改革项目[XJG2021219];山西大同大学科研基金项目[2020K2];山西省高等学校教学改革创新项目[J20220867]。

摘　　要：旋转体的体积是高等数学的重要考核内容,具有较强的应用性。文章研究了平面图形绕坐标轴及任意直线旋转所得旋转体的体积。如果平面图形具有对称性,则可利用Pappus定理简化计算过程。通过一题多解思想,拓宽学生思路,强化知识之间的联系,形成结实的知识网。The volume of revolution is an important examination content of higher mathematics,which has strong applicability.In this paper,the volume of a rotating body obtained by rotating a plane figure around a coordinate axis and any straight line is studied.If the plane figure has symmetry,the Pappus theorem can be used to simplify the calculation process.Through the idea of multiple solutions to one problem,this paper aims to broaden students'thinking,strengthen the connection between knowledge,and form a solid knowledge network.

关 键 词：旋转体 形心 柱壳法 PAPPUS定理 

分 类 号：O173[理学—数学]