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近年高考试题所提供的大量信息显示,锥体概念及多面体和旋转体的体积计算是近六年来高考的热点内容.在八十年代受冷落的柱体和球的有关概念、性质、计算已盛兴为近两年高考的热点内容.所以在复习多面体与旋转体这一章内容时,必须透切理解和掌握多面体与旋转体的有关表面积公式、体积公式,以及它们的概念和性质,注意它们的特性和联系.本文通过若干范例和联想揭示’96高考复习可以纵横联系的思想方法,探索高考的新观念、新思路,以期提高复习效果.例1.有一个实心圆锥体的零部件,它的轴截面是边长为10厘米的等边三角形,现要在它的表面镀上一层防腐材料,已知每平方厘米的工料价为0.10元,则需要费用_元(π取3.2).(’94上海高考试题)评析:这是一道数学应用的试题,关键在于求圆锥的全面积.解:依题意,得圆锥体底面半径为5厘米,母线长为10厘米.S全=πr(r+ι)=3.2×5×(5+10)=240(平方厘米).所需费用为24元.
In recent years, a large amount of information provided by the high exam questions shows that the concept of pyramids and the calculation of the volume of polyhedrons and rotating bodies are hot topics in the college entrance examination in the past six years. The concept, nature, and calculation of the cylinders and balls that were left out in the 1980s have been relentless. Hing for the hot content of the college entrance examination in the past two years. Therefore, when reviewing the contents of the polyhedron and the rotating body, we must thoroughly understand and grasp the surface area equations and volume formulae of the polyhedron and the rotating body, as well as their concepts and properties. Pay attention to them. The characteristics and connections of this article. Through a number of examples and associations, this article reveals the ’96 college entrance examination review method can be vertical and horizontal contact ideas, explore new ideas, new ideas in college entrance examination, in order to improve the review effect. Example 1. There is a solid cone parts, it The shaft section is an equilateral triangle with a side length of 10 cm. It is now to be plated with a layer of anti-corrosion material on its surface. It is known that the cost per square centimeter of material is 0.10 yuan, and the cost is _yuan (π = 3.2). (’94 Shanghai examination questions) Comment: This is a math application test, the key is to find the entire area of the cone. Solution: According to the meaning of the subject, get the cone bottom radius is 5 cm, the bus length is 10 cm. S full = Πr(r+ι)=3.2×5×(5+10)=240(cm 2 ). The required fee is 24 yuan.