坐标变换在旋转体体积和侧面积计算中的应用

The Application of Coordinate Transformation in the Calculations of the Volume and Surface Area of Rotational Solids

摘要: 旋转体的体积与侧面积计算是微积分的重要内容。本文从坐标变换的角度，重新推导了平面曲线绕不平行于坐标轴的倾斜直线旋转所得旋转体的体积和侧面积公式，为培养学生的数学思维和创新意识提供了新的教学案例。

Abstract: The calculation of the volume and lateral surface area of a solid of revolution is an important topic in calculus. This paper re-derives the formulas for the volume and lateral surface area for a solid which is obtained by rotating a plane curve around a slant line that is not parallel to the coordinate axes. These formulas are obtained from the perspective of coordinate transformation. This paper provides a new teaching case for cultivating students’ mathematical thinking and innovative consciousness.