2022年人教A版数学必修二1.3.3《空间几何体的表面积与体积》学案 .pdf

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1、名师精编优秀教案河北省邯郸四中高一数学必修2 学案：1.3.3空间几何体的表面积与体积学习目标1.会求空间几何体、简单组合体的面积和体积；2.能解决与空间几何体表面积、体积有关的综合问题；3.进一步体会把空间问题转化为平面问题的思想.学习过程一、课前准备（复习教材P23 P28，找出疑惑之处）复习 1：柱体、锥体、台体的表面积是如何求出来的？它们的体积公式有何联系？球的表面积和体积只和什么变量有关？复习 2：简单组合体的表面积和体积怎么求？二、新课导学 典型例题例 1 设圆台的上、下底面半径分别为r,r，母线长是l，圆台侧面展开后所得的扇环的圆心角是，求证：360rrlg（度）名师精编优秀教案

2、小结：有关几何体侧面的问题，通常是把侧面展开为平面图形，然后在平面图形中寻求解决途径.变式：在长方体1111ABCDA BC D 中,已知5AB,14,3BCBB,从A点出发,沿着表面运动到1C,则最短路线长是多少?小结：求立体图形表面上两点的最短距离问题，是立体几何中的一个重要题型.解决这类问题的关键是把图形展开(有时全部展开，有时部分展开)为平面图形，找出表示最短距离的线段(通常利用两点之间直线最短).例 2 若,E F 是三棱柱ABCA B C的侧棱BB和CC上的点，且B E=CF，三棱柱的体积为m,求四棱锥ABEFC的体积.变式：正三棱台ABCA B C中，12A BAB，则三棱锥AA

3、BC,BA B C,CA B C的体积比为多少?小结：当直接求体积有困难时，可利用转化思想，分割几何体，借助体积公式和图形的性质转化为其它等体积(等底等高或同底同高)的几何体，从而起到化难为易的作用.文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R

4、6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6

5、F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F

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7、5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:C

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9、7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3名师精编优秀教案 动手试试练 1.圆锥SAB的底面半径为R，母线

10、长3SAR，D为SA的中点，一个动点自底面圆周上的A点沿圆锥侧面移动到D，求 这点移动的最短距离.(在ABC中,边分别为,a b c,a 所对角为,则有2222cosabcbc)练 2.直三棱柱各侧棱和底面边长均为a，点D是CC上任意一点，连结A B、BD、AD、AD，则三棱锥AA BD的体积为多少？（）三、总结提升 学习小结1.空间问题可以转化为平面问题解决；2.最短距离的求法；3.求体积困难时可采用分割的思想，化为底（面积）高相同的规则几何体求解.知识拓展空间问题向平面的转化包括：圆锥、圆台中元素的关系问题，用轴截面来解决；空间几何体表面上两点线路最短问题，用侧面展开图来解决；球的组合体中

11、的切、接问题，用过球文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编

12、码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6

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15、档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8

16、S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O

17、4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3名师精编优秀教案心的截面来解决.学习评价 自我评价你完成本节导学案的情况为（）.A.很好 B.较好 C.一般 D.较差 当堂检测（时量：5 分钟满分：10 分）计分：1.在棱长为 1的正方体上，分别用过顶点的三条棱中点的平面截该正方体，则截去8

18、个三棱锥后，剩下多面体的体积为（）.A.23 B.76 C.45 D.562.已知球面上过,A B C 三点的截面和球心的距离是球半径的一半，且2ABBCCA，则球的表面积为（）.A.169 B.83 C.4 D.6493.正方体的 8 个顶点中有 4个恰为正四面体的顶点,则正方体的全面积与正四面体的全面积之比为（）.A.2 B.3 C.62 D.2 334.正四棱锥底面积为S，过两对侧棱的截面面积为Q，则棱锥的体积为_.5.已知圆锥的全面积是底面积的3倍，那么该圆锥的侧面展开图的圆心角_度.课后作业1.一个 圆台上下底面半径分别为5、10，母线12A A=20.一只蚂蚁从12A A 的中点M

19、绕圆台侧面转到下底面圆周上的点2A，求蚂蚁爬过的最短距离.2.已知一个圆锥的底面半径为R,高为H,在其中有个高为x 的内接圆柱.(1)求圆柱的侧面积；(2)x为何值时，圆柱的侧面积最大？文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档

20、编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S

21、6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4

22、 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3

23、文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X8S6 HU7F9V5W6O4 ZE10V5R6I9J3文档编码:CR6F8B8X

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