为落实“双减”政策中减负增效的实践作业要求，探索实现数学新课程标准中培养学生创新精神和实践能力的这一重要目标之路，渭南高新区第一小学六年级数学老师结合本学期“圆柱和圆锥”教学内容，设计了“玩转柱锥”为主题的实践作业活动。

活动一：滚一滚

利用滚动法求圆柱的侧面面积，学生通过观察滚动所形成的图形，进一步了解圆柱侧面的特性。

活动二：剪一剪

学生利用现成的圆柱模型，沿着不同方向将侧面剪开，观察比较展开图的异同点，并体验圆柱侧面积、表面积计算公式的推导过程。

活动三：切一切

学生按不同方式将生活中的“圆柱”和“圆锥”切开，探究截面，了解“截面”的产生过程，体会“面源于体”。

活动四：拼一拼

我们能把一个圆采用“化曲为直”的思想方法推导面积计算公式，同样，让学生用转化思想，通过动手实践，推导圆柱体积计算公式。

活动五：做一做

学生在了解了圆柱、圆锥特点之后，制作圆柱与圆锥创意作品，提高学生的实际操作能力，让学生充分参与到“做数学”的活动中。

活动六：画一画

圆柱与圆锥知识点多而杂，但知识点之间不是孤立的，让学生从多维度对圆柱和圆锥的知识点进行整理，找出知识点之间联系，绘制思维导图，编织自己的知识网。

此次实践活动中，同学们不断在做中学，学中思，思中悟，进一步理解了圆柱和圆锥的特征，发现了两者之间的联系和区别，发展了空间想象能力、逻辑推理能力，体会了数学的应用价值，让学生得以跳出课堂，放飞手脑，去探索更广阔的数学世界!

撰稿：冯琳

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舒玉帖3273谁能把圆锥的面积的推导过程写一下? 谢谢 很急 -
聂寇刚18484473501 ______[答案] 底面是圆形 侧面是扇形 扇形半径为斜高 central angle 为底面半径 除以圆锥斜高 乘以三百六十度 扇形面积为 central angle 除以三百六十度 乘以以斜高为半径的圆的面积 知道圆形面积怎么算就可以了

舒玉帖3273长方体、正方体、圆柱、圆锥的体积、表面积和体积公式的推导过程. -
聂寇刚18484473501 ______ 长方体: V=a·b·h=S底·高 S表=(a·b+b·c+a·c)·2 P·S·无需推导公式 正方形: V=a³=S底·高 S表=6·a² P·S·无需推导公式 圆柱: V=πr²·h S表=2πr²+2πr·h=2πr·(r+h) P·S·参见圆形推导公式(参考资料网址)就明白了.圆锥: V=πr²·h÷3=S底·高÷3 S表=无(P·S·如果老师在小学到中学要你算这个,我想你有权不算.) 体积推导公式:某某人得出“等底等高的圆锥和圆柱,圆柱的体积是圆锥的3倍”,因此而来 (不信可以做个实验,做一对等底等高的无盖圆锥和无盖圆柱,看看用圆锥装满沙子再倒进圆柱,要多少次才能把圆柱倒满.这个实验有时会失误,但成功的都是3次.)

舒玉帖3273圆柱 圆锥 的表面积和体积的公式 推到过程 数学日记 -
聂寇刚18484473501 ______[答案] 设它们的底面半径为r,高为h. 圆柱体体积:πr^2h(柱体体积等于底面积乘上高) 圆柱体表面积:2πr^2+2πrh=2πr(r+h)(底面积加侧面积) 圆锥体体积:1/3πr^2h 圆锥表面积:πr^2+1/2π2rl=πr(r+l)(l为母线长,等于根号下r的平方加h的平方)

舒玉帖3273圆锥的面积推到过程怎么推导??急需!! -
聂寇刚18484473501 ______ 圆锥的侧面展开图是一个扇形,其半径是原圆锥的母线长,设为l,其弧长为原圆锥的底面圆的周长为2πr 根据扇形的面积公式=1/2·弧长·半径 故圆锥的侧面积=1/2·2πr·l=πrl,即为圆锥的侧面积公式 如果需要全面积,则需要加上底面一个圆的面积πr^2

舒玉帖3273圆锥的表面积公式推导 -
聂寇刚18484473501 ______ 半径的平方乘3.14乘二加直径的周长乘高

舒玉帖3273圆锥体表面积公式怎样推导 -
聂寇刚18484473501 ______ 圆锥圆柱的计算公式 圆柱的侧面积=底面周长*高 圆柱的表面积=侧面积+底面积*2 圆柱的体积=底面积*高 圆锥的侧面积=高的平方*3.14*百分之扇形的度数 圆锥的表面积=底面积+侧面积 圆锥的体积=1/3*底面积*高 S侧=CH S表=S侧+2S底 V柱=SH S锥侧=H的平方*3.14*百分之扇形的度数 S锥表=S侧+S底 V锥=1/3SH

舒玉帖3273圆台的表面积公式是怎么推导出来的? -
聂寇刚18484473501 ______[答案] 首先要知道圆锥表面积S圆锥=π r l.(如果学过积分的话,这个可以用积分推倒的)然后圆台就是一个大圆锥从某一处截,截面与圆锥地面平行.然后侧面表面积就是:S圆台侧=π R l - π r l上底面面积S上= π r^2,下底面面积S下= π R^2.合起来就是圆台...

舒玉帖3273圆锥侧面积的推导过程 -
聂寇刚18484473501 ______[答案] 解前分析: ①圆锥的侧面积推导,需要把圆锥展开; ②数学上规定,圆锥的顶点到该圆锥底面圆周上任意一点的连线叫圆锥的母线; ③沿圆锥的任意一条母线剪开展开成平面图形即为一个扇形; ④展开后的扇形的半径就是圆锥的母线, 展开后的扇...

舒玉帖3273圆锥圆台表面积公式的推导过程(说说各个表面积之间怎么加的) -
聂寇刚18484473501 ______ 假设,圆台底面半径为 R ,顶面半径为 r ,台高 h ; 则假设的大圆锥体积 V1=1/3 * π * h1 * R^ ;小圆锥的体积 V2=1/3 * π * h2 * r^2 ,明显 r:R = h2:h1; 则圆台的体积 V = 1/3 * π *(h1*R*R-h2*r*r) 将 r=R * h2 /h1 代入上式 V = 1/3 * π * ((h1^3-h2^3)/h...

舒玉帖3273圆锥的面积推导过程是怎么推导的??急需!! -
聂寇刚18484473501 ______ 圆锥是圆柱的1/3.你就拿一个等底等高的圆锥和圆柱.你往圆锥里装水.然后再往圆柱里倒水.到三次倒满了.