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

","gnid":"9cdea4e97775a4804","img_data":[{"flag":2,"img":[{"desc":"","height":"800","title":"","url":"https://p0.ssl.img.360kuai.com/t014ef1fd4cfeddbcd5.jpg","width":"600"},{"desc":"","height":1837,"title":"","url":"https://p0.ssl.img.360kuai.com/t015f6882c433107fcf.jpg","width":1017},{"desc":"","height":"800","title":"","url":"https://p0.ssl.img.360kuai.com/t01ef964ec50583420d.jpg","width":"443"},{"desc":"","height":"800","title":"","url":"https://p0.ssl.img.360kuai.com/t019c67338cbee5e7a0.jpg","width":"600"},{"desc":"","height":"810","title":"","url":"https://p0.ssl.img.360kuai.com/t01cd0df185345e73b4.jpg","width":"1080"},{"desc":"","height":"608","title":"","url":"https://p0.ssl.img.360kuai.com/t01567177219798e2d6.jpg","width":"1080"},{"desc":"","height":"608","title":"","url":"https://p0.ssl.img.360kuai.com/t010f8d7fc99cfadbed.jpg","width":"1080"},{"desc":"","height":"810","title":"","url":"https://p0.ssl.img.360kuai.com/t017983d0ec6142c93d.jpg","width":"1080"},{"desc":"","height":"1280","title":"","url":"https://p0.ssl.img.360kuai.com/t0109143844d5f39a29.jpg","width":"959"},{"desc":"","height":"1279","title":"","url":"https://p0.ssl.img.360kuai.com/t01b6f44f3b4c7cb7af.jpg","width":"959"},{"desc":"","height":"800","title":"","url":"https://p0.ssl.img.360kuai.com/t010c1287b4d2fe5ec5.jpg","width":"600"},{"desc":"","height":"1080","title":"","url":"https://p0.ssl.img.360kuai.com/t01d4c16737536dce51.jpg","width":"1080"},{"desc":"","height":"800","title":"","url":"https://p0.ssl.img.360kuai.com/t0186d470b6eb7dcb56.jpg","width":"513"},{"desc":"","height":"800","title":"","url":"https://p0.ssl.img.360kuai.com/t019589412d32c09e3c.jpg","width":"600"},{"desc":"","height":"800","title":"","url":"https://p0.ssl.img.360kuai.com/t0146a102ea148c4bcb.jpg","width":"600"},{"desc":"","height":"1280","title":"","url":"https://p0.ssl.img.360kuai.com/t01561326c0519a4867.jpg","width":"960"},{"desc":"","height":"643","title":"","url":"https://p0.ssl.img.360kuai.com/t015ff7db0b5aadf68d.jpg","width":"800"},{"desc":"","height":"810","title":"","url":"https://p0.ssl.img.360kuai.com/t0195a6709858169d86.jpg","width":"1080"},{"desc":"","height":"810","title":"","url":"https://p0.ssl.img.360kuai.com/t0104873375f6d839ee.jpg","width":"1080"},{"desc":"","height":"813","title":"","url":"https://p0.ssl.img.360kuai.com/t014b9dbf7090f36f26.jpg","width":"1080"},{"desc":"","height":"602","title":"","url":"https://p0.ssl.img.360kuai.com/t01460693c28680b9f0.jpg","width":"800"},{"desc":"","height":"504","title":"","url":"https://p0.ssl.img.360kuai.com/t0179cb9033a19ba0b7.jpg","width":"800"},{"desc":"","height":"554","title":"","url":"https://p0.ssl.img.360kuai.com/t013881fb4d5a63dd0f.jpg","width":"800"},{"desc":"","height":"557","title":"","url":"https://p0.ssl.img.360kuai.com/t0185a7262c8869d5bd.jpg","width":"800"},{"desc":"","height":"570","title":"","url":"https://p0.ssl.img.360kuai.com/t0136db622720ca3224.jpg","width":"800"},{"desc":"","height":"571","title":"","url":"https://p0.ssl.img.360kuai.com/t017918621b30871258.jpg","width":"800"}]}],"original":0,"pat":"pdc,art_src_3,otherc,fts0,sts0","powerby":"cache","pub_time":1711421280000,"pure":"","rawurl":"http://zm.news.so.com/8607f70f5c83cffef4cf14c4798a9d91","redirect":0,"rptid":"700f989e6d6b1168","rss_ext":[],"s":"t","src":"渭南青年网","tag":[],"title":"渭南高新区第一小学六年级“玩转柱锥”数学实践作业展

冉牵萱3297(紧急求助)查一下球面积公式的推导, -
晁素雅18984855850 ______[答案] 让圆y=√(R^2-x^2)绕x轴旋转,得到球体x^2+y^2+z^2≤R^2. 这一段圆弧绕x轴得到的球上部分的面积近似为2π*y*ds,ds是弧长. 所以球的表面积S=∫2π*y*√(1+y'^2)dx,整理一下即得到S=4πR^2

冉牵萱3297球的表面积公式是什么? -
晁素雅18984855850 ______ 精确的球的表面积公式,是用微积分推导出来的. 精确的球的体积计算公式,也得用微积分推导出来 . 没有用立体几何算法求解的, 都是用微积分推导出来的. 精确的球的表面积计算公式: 球的表面积=4πr^2, r为球半径 ,公式唯一. 精确的球的体积计算公式: V球=(4/3)πr^3, r为球半径 ,公式唯一.

冉牵萱3297球表面积推导过程,详细过程 -
晁素雅18984855850 ______ 解法一 用^表示平方 把一个半径为R的球的上半球切成n份. 每份等高 . 并且把每份看成一个圆柱,其中半径等于其底面圆半径. 则从下到上第k个圆柱的侧面积S(k)=2πr(k)*h 其中h=R/n r(k)=根号[R^-(kh)^] S(k)=根号[R^-(kR/n)^]*2πR/n =2πR^*根号[1/...

冉牵萱3297谁能讲一讲球面积的公式是怎么推导出来的??
晁素雅18984855850 ______ 可用球的体积公式+微积分推导 定积分的应用:旋转面的面积.好多课本上都有,推导方法借助于曲线的弧长. 让圆y=√(R^2-x^2)绕x轴旋转,得到球体x^2+y^2+z^2≤R^2.求球的表面积. 以x为积分变量,积分限是[-R,R]. 在[-R,R]上任取一个子区间[x,x+△x],这一段圆弧绕x轴得到的球上部分的面积近似为2π*y*ds,ds是弧长. 所以球的表面积S=∫<-R,R>2π*y*√(1+y'^2)dx,整理一下即得到S=4πR^

冉牵萱3297球体的表面积、体积公式 -
晁素雅18984855850 ______[答案] 球体表面积计算公式为:S=4πR² 球体体积计算公式为:V=(4/3)πR³ 祝你学习愉快! 望采纳,多谢!

冉牵萱3297球的表面积、体积计算公式 -
晁素雅18984855850 ______[答案] 球的表面积计算公式:s=4πr^2,r为球半径 球的体积计算公式: v=(4/3)πr^3,r为球半径

冉牵萱3297球的表面积计算公式写出数学公式 -
晁素雅18984855850 ______[答案] 球的表面积计算公式:球的表面积=4πr^2,r为球半径 . 球的体积计算公式:V球=(4/3)πr^3,r为球半径

冉牵萱3297球体的体积和表面面积计算公式 -
晁素雅18984855850 ______[答案] 球体表面积计算公式为:S=4πR² 球体体积计算公式为:V=(4/3)πR³ 望采纳!

冉牵萱3297球体的表面积公式
晁素雅18984855850 ______ V=(4π/3)R^3,V球体积,R球半径,π:圆周率 S=4πR^2:S球面积,R球半径,π:圆周率

冉牵萱3297四面体外接球表面积公式
晁素雅18984855850 ______ 四面体外接球表面积公式:s=(a^2-b^2/3)-R.外接球意指一个空间几何图形的外接球,对于旋转体和多面体,外接球有不同的定义,广义理解为球将几何体包围,且几何体的顶点和弧面在此球上.正多面体各顶点同在一球面上,这个球叫做正多面体的外接球.三棱锥锥体的一种,几何体,由四个三角形组成.固定底面时有一个顶点,不固定底面时有四个顶点.(正三棱锥不等同于正四面体,正四面体必须每个面都是正三角形).