苏教版六年级下册圆柱和圆锥讲义.doc

专业好文档 圆柱和圆锥专题讲义【知识教学】一、圆柱的特征及表面积（一）圆柱的特征1、圆柱的认识举出生活中圆柱形状的实物2、圆柱各部分的名称圆柱的上、下两个面叫做底面，它们是面积相等的两个圆两底面之间的距离叫做高圆柱的两个底面面积相等，圆柱有无数条高（二）圆柱的侧面积和计算公式1、圆柱的侧面积圆柱的侧面积底面的周长高字母表示： sch2、侧面积公式的应用例1. 一段圆柱形的钢材，底面周长是0.28米，高是2.4米它的侧面积是多少平方米？（得数保留两位小数）sch0.282.40.6720.67（平方米）答：它的侧面积大约是0.67平方米练习：制作这个薯片筒的侧面标签，需要多大面积的纸？（三）圆柱的表面积圆柱的侧面积与两个底面积的和，就是圆柱的表面积但是实际生活中往往只求侧面和一个底面的面积的总和，比如例2. 一个没有盖的圆柱形状的铁皮水桶，高是45厘米，底面直径是34厘米做这个水桶需要多少铁皮？（得数保留整数）例3. 一个圆柱的高增加4厘米，表面积增加50.24平方厘米，求圆柱体的底面积分析：圆柱的高增加4厘米，表面积增加50.24平方厘米，50.24平方厘米就是高是4厘米的圆柱的侧面积，根据这两个条件可以求出圆柱的底面周长，从而求出圆柱的底面积练习1：一个圆柱形水池，水池内壁和底面都要镶上瓷砖，水池底面直径6米，池深1.2米。镶瓷砖的面积是多少平方米？二、圆柱、圆锥的体积（一）圆锥的认识像蛋卷、草帽这样的形体都是圆锥,圆锥是由哪几部分组成的呢？各有什么特点?圆柱体有高，而且有无数条；圆锥体有高吗？有多少条？有，只有一条（二）圆柱的体积圆柱的体积底面积高用字母表示： 下面应用公式做一道题例4. 有一根圆柱形状的塑料棒，它的横截面的面积是24平方厘米，长是0.9米这根塑料棒的体积是多少立方厘米？0.9米90厘米24902160（立方厘米）答：这根塑料棒的体积是2160立方厘米例5. 如图所示，一块长方形铁皮，利用图中的阴影部分刚好做一个油桶（接头处忽略不计）求这个油桶的容积分析：长方形铁皮的宽相当于两个底面直径，所以只能做油桶的高，长方形铁皮的长是16.56分米，正好是直径的（3.14+1）倍，从而可以求出直径的长，进而求出油桶的容积例6. 一只装水的圆柱形玻璃杯，底面积是80平方厘米，水深8厘米现将一个底面积是16平方厘米的长方体铁块竖放在水中后，仍有一部分铁块露在外面现有水深多少厘米?分析：圆柱形玻璃杯底面积是80平方厘米，水深8厘米，根据这两个条件可以求出水的体积，如果将一个底面积是16平方厘米的长方体铁块竖放在水中后，仍有一部分铁块露在外面，那么相当于容器的底面积减少16平方厘米，也就是还剩下80-1664平方厘米，把原来的水放进底面积是64平方厘米的容器中，水深就很容易求出来了808640（立方厘米）80-1664（平方厘米）6406410（厘米）答：现有水深10厘米练习1：把一个长8厘米、宽6厘米、高4厘米的长方体木块削成一个最大的圆柱体积木，这个圆柱体积木的体积是多少立方厘米？练习2：一个饮料瓶的瓶身呈圆柱形，容积为250毫升。当瓶子正放时饮料高16厘米；当瓶子倒放时空余部分高4厘米（如右图）。请你算一算瓶内饮料为多少毫升？（三）圆锥的体积圆锥体的体积用字母表示： 例7. 一个圆锥形状的零件，底面积是12.3平方厘米，高是5厘米这个零件的体积是多少立方厘米？12.3561.520.5（立方厘米） 答：这个零件的体积是20.5立方厘米练习1. 一个近似于圆锥形状的沙堆，测得底面直径4米，高1.5米。每立方米沙大约重1.7吨，这堆沙约重多少吨？（得数保留整吨数）练习2. 如图，先将甲容器注满水，再将水倒入乙容器，这时乙容器中的水有多高？（单位：厘米）思考题：一个直角三角形（如下图），分别以两条直角边所在的直线为轴，旋转成两个圆锥体，哪个圆锥体的体积大？为什么？（单位：厘米）二、公正法官。1.圆柱和圆锥都只有一条高。（ ）2.任何一个圆柱都是由两个平面和一个曲面围成的立体图形。（ ）3.从圆锥的顶点向底面作垂直切割，所得到的横截面是一个等腰三角形。（ ）三、精挑细选。1.油漆大厅的圆柱形柱子，就是求柱子的（ ）a侧面积b表面积c.底面周长2.一个圆柱形水池，底面直径是8米，深是2.5米，求这个水池的占地面积的计算式是（ ）3.把一张正方形铁皮卷成一个圆柱筒，这个圆柱筒的（ ）a高与底面直径相等b底面周长是高的倍c高与底面积相等d高与底面周长相等4在下图中，以直线为轴旋转，可以得到圆柱的是（ ）四、生活百花园。1如右下图，做一对这样的“美味鲜蚝油”罐，需要多少铁皮？（铁皮的接头处忽略不计）2压路机的滚筒是个圆柱，它的宽是2米，滚筒横截面半径是0.6米，如果滚筒每分钟滚动5周，那么1小时可压路多少平方米？3一种圆柱形通风管，长是2米，管口半径是4分米。做10根这样的通风管至少需要多少铁皮？4用塑料绳捆扎一个圆柱形的蛋糕盒（如右下图），打结处正好是底面圆心，打结用去绳长10厘米。(1)扎这个盒子至少用去塑料绳多少厘米？ 20厘米(2)在它的整个侧面贴上商标和说明，这部分的面积至少是多少平方厘米？5.右下图，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。这个物体的表面积是多少平方米？6求下面空心零件的表面积和体积。（单位：厘米）7把两个底面直径都是4厘米、长都是3分米圆柱形钢材焊接成一个大的圆柱形钢材，焊接成的圆柱形钢材的表面积比原来两个小圆柱形钢材的表面积之和减少了多少？8.将一个高为8厘米的圆柱，沿着它的直径将它剖成两个半圆柱，表面积增加了96平方厘米。求半圆柱的表面积？9.右下图是一顶帽子。帽顶部分是圆柱形，用黑布做；帽沿部分是一个圆环，用白布做。知果帽顶的半径、高与帽沿的宽都是a厘来，那么哪种颜色的布用得多？winger tuivasa-sheck, who scored two tries in the kiwis 20-18 semi-final win over england, has been passed fit after a lower-leg injury, while slater has been named at full-back but is still recovering from a knee injury aggravated against usa.both sides boast 100% records heading into the encounter but australia have not conceded a try since josh charnleys effort in their first pool match against england on the opening day.aussie winger jarryd hayne is the competitions top try scorer with nine, closely followed by tuivasa-sheck with eight.but it is recently named rugby league international federation player of the year sonny bill williams who has attracted the most interest in the tournament so far.the kiwi - with a tournament high 17 offloads - has the chance of becoming the first player to win the world cup in both rugby league and rugby union after triumphing with the all blacks in 2011.id give every award back in a heartbeat just to get across the line this weekend, said williams.the (lack of) air up there watch mcayman islands-based webb, the head of fifas anti-racism taskforce, is in london for the football associations 150th anniversary celebrations and will attend citys premier league match at chelsea on sunday.i am going to be at the match tomorrow and i have asked to meet yaya toure, he told bbc sport.for me its about how he felt and i would like to speak to him first to find out what his experience was.uefa hasopened disciplinary proceedings against cskafor the racist behaviour of their fans duringcitys 2-1 win.michel platini, president of european footballs governing body, has also ordered an immediate investigation into the referees actions.cska said they were surprised and disappointed by toures complaint. in a statement the russian side added: we found no racist insults from fans of cska. baumgartner the disappointing news: mission aborted.the supersonic descent could happen as early as sunda.the weather plays an important role in this mission. starting at the ground, conditions have to be very calm - winds less than 2 mph, with no precipitation or humidity and limited cloud cover. the balloon, with capsule attached, will move through the lower level of the atmosphere (the troposphere) where our day-to-day weather lives. it will climb higher than the tip of mount everest (5.5 miles/8.85 kilometers), drifting even higher than the cruising altitude of commercial airliners (5.6 miles/9.17 kilometers) and into the stratosphere. as he crosses the boundary layer (called the tropopause),e can expect a lot of turbulence.the balloon will slowly drift to the edge of space at 120,000 feet ( then, i would assume, he will slowly step out onto something resembling an olympic diving platform.they blew it in 2008 when they got caught cold in the final and they will not make the same mistake against the kiwis in manchester.five years ago they cruised through to the final and so far history has repeated itself here - the last try they conceded was scored by englands josh charnley in the opening game of the tournament.that could be classed as a weakness, a team under-cooked - but i have been impressed by the kangaroos focus in their games since then.they have been concentrating on the sort of stuff that wins you tough, even contests - strong defence, especially on their own goal-line, completing sets and a good kick-chase. theyve been great at all the unglamorous stuff tha