圆锥的体积计算公式

圆锥的体积计算公式 圆 锥 的 体 积 计 算 教 案 教学:圆锥的体积计算公式(人教版第十二册课本第42至43页的内容。) 教学目标: 1、使学生理解和掌握圆锥体积的计算公式，会计算圆锥的体积，并能应用所学的知识解决有关的生活实际问题。 2、培养学生的观察、发现、猜想、实践能力及合作探究意识。 教学重点:圆锥的体积计算。 教学难点:圆锥的体积公式推导。 教具准备:多媒体课件 教学过程: 一、 复习引入 (口答圆柱体积的计算公式。 1 2(求下面各圆柱的体积。 ?底面积是5平方厘米，高6厘米，体积 =? ?底面半径是2分米，高10分米，体积 =? ?底面直径是6分米，高10分米，体积 =? 3(谈话引入课题,并出示课题。 ?我们已知道了哪些立体图形体积的求法, ?我们是用怎样的方法推断出圆柱的体积的计算公式, 二、探究新知 1、指导探究圆锥体积的计算公式( 师:大家觉得我们今天研究的圆锥的体积可能转化为什么来研究呢,(圆柱) 下面我们就来看一下下面的圆柱和圆锥，判断一下这一对圆锥和圆柱有什么关系 coefficient not greater than 1.3; High efficiency: control 1 hour travel time between any two points within the various groups within the area up to half an hour, 1-hour access to the airport, 45min reached the city's main traffic hub, external highway for half an hour with the main channels connecting bus 1.5 hours between any two groups of core areas; Intensive: 2030 transit share rate of around 35%, 2050 bus sharing rate of 45% per cent. 3rd chapter, Yibin city, traffic situation and General ... 3.1.1 city traffic status 1, external transport passenger and cargo traffic in Yibin city, traffic at the present main railway, highway, waterway and air four modes of passenger and freight transport, there 师:等底等高的圆柱体和圆锥体，底面积和高都相等，它们的体积之间存在怎样的关系呢,谁能猜猜看～ (生:圆柱体的体积是圆柱体积的二分之一、三分之一、三分之二。) 师:同学们估计的都不错，但其中只有一种是对的，是那一种呢,现在我们来看一下老师课件的展示(老师展示并述说展示的过程) 师:谁能根据老师的演示把自己发现给大家介绍一下, (生:圆柱体积是与它等底等高的圆锥体积的3倍。或者说:圆锥体积是与它等底等高的圆柱体积的三分之一。) 师:同学们说的真好， 先让我们想想这个圆柱的体积公式～ 如果用V表示体积，S表示底面积，H表示高，它的体积怎么表示, 我们展示的这个圆锥体的底面积是S，高是h,它的体积是多少, (学生思考、讨论。) 师:谁能把自己的想法说给大家听, 让学生说说自己的想法。 师:同学们发现的算法可多了，也让老师大开眼界。谁能将这些算法，总结出一个计算圆锥体的体积公式呢, 师生共同总结圆锥体体积的计算公式: 圆锥体积=底面积×高× 用字母表示: V = SH 师:在这个公式里，三分之一表示什么意思,V表示什么意思,H表示什么意思,S表示什么意思,SH表示什么意思, (圆锥体积是与它等底等高的圆柱体积的三分之一) 师:同学需要注意的是我们研究的圆锥与圆柱是什么样的关系～(等底等高) 师:现在我们再想一想要求圆锥的体积必须知道什么,(底面积和高) 师:下面请同学口答两题 (1)一个圆柱体积是27立方分米,与它等底等高的圆锥体积是多少立方分米? coefficient not greater than 1.3; High efficiency: control 1 hour travel time between any two points within the various groups within the area up to half an hour, 1-hour access to the airport, 45min reached the city's main traffic hub, external highway for half an hour with the main channels connecting bus 1.5 hours between any two groups of core areas; Intensive: 2030 transit share rate of around 35%, 2050 bus sharing rate of 45% per cent. 3rd chapter, Yibin city, traffic situation and General ... 3.1.1 city traffic status 1, external transport passenger and cargo traffic in Yibin city, traffic at the present main railway, highway, waterway and air four modes of passenger and freight transport, there (2) 一个圆锥体积是15立方厘米,与它等底等高的圆柱体积是多少立方厘米? 2、运用公式教学例题 (1)出示例1 一个圆锥形零件,底面积是19平方厘米,高12厘米。这个零件的体积是多少? 学生尝试练习,教师讲评 ×19 ×12=76(立方厘米) 答:这个零件的体积是76立方厘米( (2)出示例2。 在打谷场上,有一个近似于圆锥形的小麦堆,测得底面直径是4米,高是1.2米。每立方米小麦约重735千克,这堆小麦大约有多少千克?(得数保留整千克) 学生读题思考片刻后:要求小麦重量,须先求出什么?然后学生尝试练习,个别板演,教师讲评。 三、巩固练习 1、填空: (1)、圆锥的体积=( )，用字母表示是( )。 (2)、圆柱体积的与和它( )的圆锥的体积相等。 (3)、一个圆柱和一个圆锥等底等高，圆柱的体积是3立方分米，圆锥的体积是( )立方分米。 (4)、一个圆锥的底面积是12平方厘米，高是6厘米，体积是( )立方厘米。 2、判断: (1)、圆柱体的体积一定比圆锥体的体积大。 (2)、圆锥的体积等于和它等底等高的圆柱体的。 (3)、正方体、长方体、圆锥体的体积都等于底面积×高。 (4)、等底等高的圆柱和圆锥，如果圆柱体的体积是27立方米，那么圆锥的体积是9立方米。 3、课本第43页“做一做”第1、2题。学生尝试练习,个别板演,教师讲评。 四、小结 coefficient not greater than 1.3; High efficiency: control 1 hour travel time between any two points within the various groups within the area up to half an hour, 1-hour access to the airport, 45min reached the city's main traffic hub, external highway for half an hour with the main channels connecting bus 1.5 hours between any two groups of core areas; Intensive: 2030 transit share rate of around 35%, 2050 bus sharing rate of 45% per cent. 3rd chapter, Yibin city, traffic situation and General ... 3.1.1 city traffic status 1, external transport passenger and cargo traffic in Yibin city, traffic at the present main railway, highway, waterway and air four modes of passenger and freight transport, there 今天这节课,你学到了什么知识?要求圆锥的体积需要知道哪些条件? 你对自己掌握的知识满意吗?你给自己打了多少分 五、作业 练习九的第3-5题。 coefficient not greater than 1.3; High efficiency: control 1 hour travel time between any two points within the various groups within the area up to half an hour, 1-hour access to the airport, 45min reached the city's main traffic hub, external highway for half an hour with the main channels connecting bus 1.5 hours between any two groups of core areas; Intensive: 2030 transit share rate of around 35%, 2050 bus sharing rate of 45% per cent. 3rd chapter, Yibin city, traffic situation and General ... 3.1.1 city traffic status 1, external transport passenger and cargo traffic in Yibin city, traffic at the present main railway, highway, waterway and air four modes of passenger and freight transport, there