(完整word版)2019-2020年高三数学上册15.3《旋转体的概念》学案沪教版.pdf
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1、2019-2020 年高三数学上册 15.3 旋转体的概念学案沪教版一 旋转体定义:一条平面曲线(包括直线)绕它所在的平面内的一条定直线旋转所形成的曲面叫 旋转面。这线叫 旋转轴。无论旋转到什麽位置这条曲线叫旋转面的母线。封闭的旋转面围成的几何体叫旋转体。旋转面的轴叫 旋转体的轴。二 几种常见的旋转体定义:矩形绕一边旋转一周所围成的几何体叫圆柱。绕一直角边旋转一周所围成的几何体叫圆锥。直角梯形绕垂直于底边的腰旋转一周所围成的几何体叫圆台圆绕它的直径旋转一周所围成的几何体叫球。注意:(1)垂直于轴的线段绕轴旋转一周形成圆面。(2)与轴相交的直线绕轴旋转一周形成圆锥面。(3)与轴平行的直线绕轴旋转
2、一周形成圆柱面。(4)不平行也不相交的线段绕轴旋转一周形成圆台面。折线旋转形成上锥、下台2性质圆柱圆锥圆台球底 面平行且全等的圆圆 面相 似 的 两 个 圆面轴 线过底面圆心且垂直底面过顶点和底面圆心垂直于底面过 上 下 底 面 圆心且垂直底面过球心母 线平行且相等且垂直于底面相交于一点延 长 线 交 于 一点大圆(过球心)小圆(不过球心轴 截 面全等的矩形,两边是母线,另两边是两底直径全等的等腰三角形全等的等腰梯大圆平 行 于 底 面的截面全等的圆与底面相等相似的圆(比例关系)圆球 心 和 截 面 圆 圆心连线垂直截面侧面展开图矩形扇形扇环三、体中各元素间的关系上述个体中各元素间的关系是通过
3、三角形、矩形、梯形、圆、扇形等来体现O O O O1O1A1A1V A A A 精品资料-欢迎下载-欢迎下载 名师归纳-第 1 页,共 7 页 -的。这些关系是求体积、表面积及其它有关问题的有力依据。1正 n 棱柱(n3)侧面展开图 h=l=三个矩形:ABB1A1 ,AOO1A1 ,GOO1G1 两个直角三角形:RtO1A1G1 RtOAG,2正 n棱锥侧面展开图四个直角三角形:;(1)RtVOA (2)RtVOF (3)RtVAF (4)RtOAF 3正 n棱台三个直角梯形:(1)梯形 OO1A1B (2)梯形 OO1E1E (3)梯形 EE1B1B 两个相似三角形:RtOBE Rt O1B
4、1E1;=;=4圆柱D C1A1D1C B A a d r E h l B1EO OA D C B l h O1Or 侧面展开图2r 红色为轴截面r d G A B C h B1 G1 A1 O1 O l F A B r d E O C D V h l l 精品资料-欢迎下载-欢迎下载 名师归纳-第 2 页,共 7 页 -文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W
5、3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8
6、HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W
7、9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2
8、ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5
9、A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7
10、文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:C
11、S10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7矩形 OO1BA h=l 矩形 ABCD AD=BC=2r BD=S圆柱侧=S矩 ABCD=2 rlBD是从 B绕圆柱侧面一周到A的最短距离5圆锥:一个三角形及一个扇形RtOPA中扇形中 =C=2 r ;=;=2lsin 为从 A出发绕圆锥侧面一周再回到A的最短距离 S 圆锥侧=S扇=rl=cl 6圆台:一个梯形及一个扇环。(可恢复成锥)直角梯形中扇环中 =2=C;=2r=C;=S圆台侧=S扇环=(r+)l=(c+)l 为从绕圆台一周到A的
12、最近距离。证明:由比例性质=lrrlrrrrlr)(22207球:两个直角三角形PBAOrhl侧面展开图红色为轴截面O A r h l 侧面展开图B 红色为轴截面精品资料-欢迎下载-欢迎下载 名师归纳-第 3 页,共 7 页 -文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8
13、HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W
14、9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2
15、ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5
16、A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7
17、文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:C
18、S10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W
19、3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7RtABC中 =(R+d)(R-d)=2R(R+d)=2R(R-d)+=4 RtAO1O中=+四、表面积和体积公式1球冠定义:球面被平面所截得的一部分叫做球冠,球冠也可以看作一段圆弧绕经过它的一个端点直径旋转所成的曲面。S球冠=2 Rh(舍)2球缺定义:一个球被平面剪下的一部分叫做球缺。V球缺=h2(3R-h)(舍)h:球缺的高;R:球的半径。正棱台侧面积公式 S正棱台侧 =(c+)c=0 S正棱柱侧 =c S正棱锥侧 =c 圆台侧面积公式 S圆台侧 =(c+)l=(R+r)l c=(r=R)=0(r=0)S圆柱侧 =cl=2Rl S
20、圆锥侧 =ch=Rl 台体的体积公式 V台=h(s+)s=0 V柱=sh V锥=sh 圆台的体积公式 V圆台=h(r2+2+r)r=0 V圆柱=r2h V圆锥=r2h 球冠表面积:S球冠=2 Rh h=2R S球=4 R2 球缺体积:V球缺=h2(3R-h)h=2R V球=R3=d3 五、球面距离在球面上两点之间的最短距离就是经过这两点的大圆在这两点间的一段劣弧的长度,这个弧长叫两点间球面距离。O P Q O A B K 40经度纬度精品资料-欢迎下载-欢迎下载 名师归纳-第 4 页,共 7 页 -文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:C
21、S10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W
22、3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8
23、HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W
24、9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2
25、ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5A5S1C7文档编码:CS10P9W3F5K8 HF4M4W9S1M2 ZT10S5
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