曲边扇形绕平面斜轴的旋转体体积

Volume of Solid of Revolution formed by Revolving Curvilinear Sector around Tilted Axis

根据微积分的有关知识,利用坐标平移的方法,对极坐标系下的曲边扇形绕任意平面斜轴的旋转体体积公式进行分析,得到旋转轴不经过极点时旋转体体积的计算方法,并借助实例进行说明.

Based on the knowledge of calculus and the method of coordinate translation,the formula for the volume of the solid of revolution by revolving the curvilinear sector around the tilted axis in polar coordinate system is analyzed.A formula for calculating the volume of the solid of revolution is obtained when the tilted axis does not pass through the pole.An examples is provided to demonstrate the application of the formula.