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1、圆柱和圆锥第一部分基础部分一、圆柱和圆锥的认识1、图形的形成圆柱是以长方形的一边为轴旋转而得到的，也可以由长方形（或正方形）卷曲而得到；圆锥是以直角三角形的一直角边为轴旋转而得到的，圆锥也可以由扇形卷曲而得到。2、高的条数：圆柱有无数条高；圆锥只有一条高3、侧面展开图圆柱：沿着高展开,展开图形是长方形，长方形的长等于圆柱底面的周长，长方形的宽等于圆柱的高，当底面周长和高相等时（h=2R），侧面沿高展开后是一个正方形，展开图形为正方形。圆锥：侧面展开得到一个扇形4、图形的形成：（1）圆柱：卷曲：也可以由长方形（或 正方形）卷曲而得到；旋转：圆柱是以长方形的一边为轴旋转而得到的（2）圆锥：卷曲：也
2、可以由扇形卷曲而得到；旋转：以直角三角形的一条直角边为轴旋转得到【例 1】：下面（）图形是圆柱的展开图。（单位：cm）【易错题】一个圆柱的侧面沿高展开是一个长12.56CM，宽 6.28CM的长方形，求这个圆柱的底面半径。【例 2】在下图中，以直线为轴旋转，可以得出圆柱体的是（）【易错题】1、把长为 5cm.宽为 3cm的长方形旋转成一个圆柱，则这个圆柱的表面积是多少平方厘米？2、把两条直角边分别是5cm和 3cm的直角三角形旋转成一个圆锥，这个圆锥的体积是多少立方厘米？【练习：】一、选择1、圆柱侧面积的大小是由（）决定的。A 圆柱的底面周长B 底面直径和高C 圆柱的高。2、下面的材料中，（）
3、能做成圆柱。1 号2 号3 号4 号5号A.1 号、2 号和 3 号B.1 号、4 号和 5 号C.1 号、2 号和 4 号二、解答题一个长为 8m,宽为 6m 的长方形旋转成一个圆柱，它的侧面积是多少平方米？二、圆柱表面积的计算方法公式：圆柱的表面积 S表=S侧+S底2=2rh+2 r2圆柱表面积计算公式的运用运用 1：已知圆柱的底面半径和高，求圆柱的表面积；12cm 6.28cm 2cm 2cm 4cm 4cm 文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4
4、P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 Z
5、O8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4
6、P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 Z
7、O8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4
8、P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 Z
9、O8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4
10、P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3运用 2：已知圆柱的底面直径和高，求圆柱的表面积；运用 3：已知圆柱的底面周长和高求圆柱的表面积。拓展提升：运用 4：已知侧面积和高求圆柱的表面积【例】一个圆柱的侧面积是94.2cm2，高是 10cm，求它的表面积。运用 5：已知底面积和高求圆柱的表面积【例】一个圆柱的底面积是12.56m2，高是 5cm，求它的表面积。【练习】：1、一个圆柱的侧面积是62.8cm2，高是 10cm，这个圆柱的表面积是多少平方厘米？2、一个圆柱的底面积是28.26cm2，高是 10cm，这个圆柱的表面积是多少平方厘米？根据实际情况计算圆柱的表面积常见的
11、圆柱解决问题：、压路机压过路面面积、烟囱、教学楼里的支撑柱、通风管、出水管（求侧面积）；、压路机压过路面长度（求底面周长）；、水桶铁皮（求侧面积和一个底面积）；鱼缸、厨师帽（求侧面积和一个底面积）；练习：1、选择：在手工课上小明用纸板做一个圆柱形笔筒，要求出小明用了多少平方厘米纸板，实际上就是求这个笔筒的（）A.侧面积 B.侧面积+2个底面积 C.侧面积+1 个底面积2、生活运用题：祈年殿是北京天坛公司的主要建筑，中央4 根龙柱高 19.2 米。直径是 1.2 米，象征四季。如果把每根龙柱的表面刷一层油漆，粉刷的面积是多少平方米？三、圆柱和圆锥的体积文档编码:CD9Q4P4A3S9 HZ5T1
12、W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档
13、编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1
14、W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档
15、编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1
16、W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档
17、编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1
18、W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P31、圆柱：V柱Sh=r2h 圆柱体积公式的推导：把圆柱平均分成若干个扇形，然后拼成一个近似的长方体，长方体的长等于圆柱（），长方体的宽等于圆柱（），长方体的高等于圆柱的（）；V柱 =【体积公式推导的应用】1、把一个圆柱底面平均分成若干个扇形，沿高切开拼成一个近似长方体，这个长方体的长是 6.28 厘米，高是 5 厘米，求它的体积。2、一个圆柱体的体积是50.24立方厘米，底面半径是2 厘米将它的底面平
19、均分成若干个扇形后，再截开拼成一个和它等底等高的长方体，表面积增加了多少平方厘米？(3.14)考试常见题型：a 已知圆柱的底面积和高，求圆柱的侧面积，表面积，体积，底面周长b 已知圆柱的底面周长和高，求圆柱的侧面积，表面积，体积，底面积c 已知圆柱的底面周长和体积，求圆柱的侧面积，表面积，高，底面积d 已知圆柱的底面面积和高，求圆柱的侧面积，表面积，体积，e 已知圆柱的侧面积和高，求圆柱的底面半径，表面积，体积，底面积f、V钢管=【例 1】：计算下面各圆柱体的体积。A、底面积是 1.25 平方米，高 3 米。B、底面直径和高都是8 分米。C、底面半径和高都是8 分米。D、底面周长是 12.56
20、 米，高 2 米。【例 2】求下面立体图形的体积，以及制作这么一个物体所用的铁皮面积。文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9
21、HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V
22、8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9
23、HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V
24、8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9
25、HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V
26、8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P32、圆锥：V锥=31底面积高31Sh 31r2h圆锥体积的推导：（注意：等底等高 的圆柱和圆锥。）V锥=考试常见题型：a 已知圆锥的底面积和高，求体积b 已知圆锥的底面周长和高，求圆锥的体积，底面积c 已知圆锥的底面周长和体积，求圆锥的高，底面积【例】：1、求下列圆锥体积（
27、1）底面积是 7.8 平方米，高是 1.8 米（2）底面半径 4 厘米，高 21 厘米（3）底面周长是 12.56 米，高 4 米第二部分典型题型总结一、巧求表面积1、组合图形的表面积=【例】如图所示，将高都是1 米，底面半径分别为1.5 米、1 米和 0.5 米的三个圆柱组成一个物体。求这个物体的表面积。1110.511.52、挖空问题【例】有一个圆柱体的零件，高10 厘米，底面直径是 6 厘米，零件的一端有一个圆柱形的圆孔，圆孔的直径是4 厘米，孔深 5 厘米（见右图）。如果将这个零件接触空气的部分涂上防锈漆，那么一共要涂多少平方厘米？文档编码:CD9Q4P4A3S9 HZ5T1W4L1E
28、9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD
29、9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E
30、9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD
31、9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E
32、9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD
33、9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E
34、9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P33、不规则物体的表面积和体积【例】求下面物体的侧面积和体积（单位：厘米）练习：1、一个底面直径是 6 厘米，高为 8 厘米的圆柱体，叠在底面直径是12 厘米、高是 12 厘米的圆柱体上，求这个物体的表面积。2、一个棱长为 40 厘米的正方体零件（如图27-11 所示）的上、下两个面上，各有一个直径为 4 厘米的圆孔，孔深为10 厘米。求这个零件的表面积。3、求下图的侧面积和体积。（单位：米）二、等量转换问题：【
35、例】两个底面积相等的圆柱，一个圆柱的高是7 分米，体积是 54 立方分米，另一个圆柱的高 5 分米，另一个圆柱的体积是多少立方分米？练习：1、一个圆锥形沙堆，底面周长是 12.56 米，高是 4.8 米，用这堆沙在 10 米宽的公路上铺 2 厘米厚，能铺多少米长？文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9
36、Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9
37、 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9
38、Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9
39、 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9
40、Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9
41、 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P32、把一个底面半径是6 厘米，高是 10 厘米的圆锥形容器灌满水，然后把水倒入一个底面半径是 5
42、 厘米的圆柱形容器里，求圆柱形容器内水面的高度？三、圆柱和圆锥的关系（1）等底等高：V锥:V 柱1:3；圆柱体积比等底等高圆锥体积多2 倍；圆锥体积比等底等高圆柱体积少32（2）等底等体积：h 锥:h 柱3:1 （3）等高等体积：S锥:S 柱3:1 方法总结：1、等底等高时：圆柱体积是圆锥体积的3 倍 2、等体积等高（或底）时：圆锥的底（或高）是圆柱的3 倍【例 1】一个圆柱体和一个圆椎体的底面积和高相等，已知圆柱体的体积是7.8立方米，那么圆椎体的体积是（）立方米【例 2】一个圆柱体和一个圆锥体等底等高，它们的体积相差50.24 立方厘米。如果圆锥体的底面半径是2 厘米，这个圆锥体的高是多少
43、厘米？【例 3】一个圆锥的体积与它等底等高的圆柱的体积的和是24cm3，这个圆柱的体积是（）【例 4】一个圆柱体和一个圆椎体的底面积和体积相等，圆柱的高是12cm，圆锥的高是（）。【例 5】一个圆柱体和一个圆椎体的体积和高相等，圆锥的底面积是12 平方米，圆柱的底面积是（）练习：1、把一段圆柱形的木料削成一个最大的圆锥，削去部分体积是圆锥体积的（）2、一个圆锥的体积比与它等底等高的圆柱的体积少54cm3，这个圆柱的体积是（）3、一个体积是 24 立方米，底面积是 8 平方米的圆柱与一个圆锥等体积等高，圆锥的底面积是（）米，四、比例扩大缩小问题核心思想：运用公式解决比例问题【例1】圆锥的底面积扩
44、大 2倍，高不变，它的体积（）【例 2】有两个底面半径相等的圆柱，高的比是2：5。第二个圆柱的体积是175立方厘米，第二个圆柱的体积比第一个圆柱多多少立方厘米？【例 3】甲乙两个圆柱，底半径比是 2：3,高的比是 4：5,它们的体积比是多少？练习：1、圆锥的底面半径和高都缩小2倍，它的体积就（）文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8
45、T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4
46、A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8
47、T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4
48、A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8
49、T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4
50、A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P3文档编码:CD9Q4P4A3S9 HZ5T1W4L1E9 ZO8T1Y6V8P32、圆柱的底面直径扩大2 倍，高缩小为原来的1/2，那么圆柱的侧