圆柱、圆锥常用的表面积、体积公式

圆柱、圆锥常用的表面积、体积公式 圆柱与圆锥 例题精讲 圆柱、圆锥常用的表面积、体积公式 立体图形 表面积 体积 22 Srhr,，,，侧面积个底面积22π2πVrh,π圆柱圆柱h r圆柱 n1222 Slr,，,，侧面积底面积ππVrh,π圆锥圆锥体h3603r l注:是母线～即从顶点到底面圆上的线段长 圆锥 板块一 圆柱与圆锥 1.50.53【例 1】 如图，用高都是米，底面半径分别为米、米和米的个圆柱组成一个物体(问这个物体的11 3.14取) 表面积是多少平方米,(π 10.5 1 1 1 1.5 106【例 2】 有一个圆柱体的零件，高厘米，底面直径是厘米，零件的一端有一个圆柱形的圆孔，圆孔的直 5径是厘米，孔深厘米(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4 少平方厘米, 【例 3】 (第四届希望杯2试)圆柱体的侧面展开，放平，是边长分别为10厘米和12厘米的长方形，那 π么这个圆柱体的体积是________立方厘米((结果用表示) Otherwise the pump should be checked again to install. 4.2.5.1 structure embedded phase 1, toilet drain structure places a waterproof steel bushings, measure width of the beam, use galvanized steel pipe welding and sealing rings, measure elevation on positions in the structure main bars of beams, welded prison using sawdust block. Hole thin iron sleeve construction, length about 200 mm, easy installation and handle construction, casing used touch Remover (available used oil paint), Eachd8, transfer and underground drainage pipe installation mounting, hang-dry pipe must first make an outline, the carrier according to the design of slope planted well hung code, pipe hangers, prefabricated piping Bay and state provision and other sanitary and drainage provision for finding sizes, clamp the connection interface. The connection between the pipe and the main pipe to ensure smooth, sloping according to design requirements, no camber behavior occurs. Buried trunk pipe supporting frame, before you install DUN, planted well pipe sizes, will be reserved for finding and fixed the pipe size, and then sealing with cement mortar. 9, after the construction of water testing, water testing and well outside through-ball after completion of construction. 10, construction notes: when using metal pipe clamps, 【例 4】 如右图，是一个长方形铁皮，利用图中的阴影部分，刚好能做成一个油桶(接头处忽略不计)，求这 π,3.14个油桶的容积(() 16.56m 【巩固】如图，有一张长方形铁皮，剪下图中两个圆及一块长方形，正好可以做成1个圆柱体，这个圆柱体 π,3.14的底面半径为10厘米，那么原来长方形铁皮的面积是多少平方厘米,() 10cm 【例 5】 把一个高是8厘米的圆柱体，沿水平方向锯去2厘米后，剩下的圆柱体的表面积比原来的圆柱体表 12.56面积减少平方厘米(原来的圆柱体的体积是多少立方厘米, 50.24【巩固】一个圆柱体底面周长和高相等(如果高缩短4厘米，表面积就减少平方厘米(求这个圆柱体的 表面积是多少, 4cm 【例 6】 (2008年第二届两岸四地”华罗庚金杯”少年数学精英邀请赛)一个圆柱体形状的木棒，沿着底面直22008cm径竖直切成两部分(已知这两部分的表面积之和比圆柱体的表面积大，则这个圆柱体木棒23.14cmπ的侧面积是________((取) 2ball after completion of construction. 10, construction notes: when using metal pipe clamps,-throughtside xed the pipe size, and then sealing with cement mortar. 9, after the construction of water testing, water testing and well ouurs. Buried trunk pipe supporting frame, before you install DUN, planted well pipe sizes, will be reserved for finding and fior ocche connection between the pipe and the main pipe to ensure smooth, sloping according to design requirements, no camber behaviOtherwise the pump should be checked again to install. 4.2.5.1 structure embedded phase 1, toilet drain structure places a wapiping Bay and state provision and other sanitary and drainage provision for finding sizes, clamp the connection interface. Tbricated dry pipe must first make an outline, the carrier according to the design of slope planted well hung code, pipe hangers, prefa-used touch Remover (available used oil paint), Eachd8, transfer and underground drainage pipe installation mounting, hangasing on using sawdust block. Hole thin iron sleeve construction, length about 200 mm, easy installation and handle construction, cvanized steel pipe welding and sealing rings, measure elevation on positions in the structure main bars of beams, welded pristerproof steel bushings, measure width of the beam, use gal |初一?数学?基础-提高-精英?学生版| 第1讲 第页 第2题1040【巩固】已知圆柱体的高是厘米，由底面圆心垂直切开，把圆柱分成相等的两半，表面积增加了平方厘 π,3米，求圆柱体的体积(() 50.24【例 7】 一个圆柱体的体积是立方厘米，底面半径是2厘米(将它的底面平均分成若干个扇形后，再 π,3.14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, () 【例 8】 右图是一个零件的直观图,下部是一个棱长为40cm的正方体,上部是圆柱体的一半,求这个零件 的表面积和体积, 2.5【例 9】 输液100毫升，每分钟输毫升(如图，请你观察第12分钟时图中的数据，问:整个吊瓶的容积 是多少毫升, 【例 10】 (2008年”希望杯”五年级第2试)一个拧紧瓶盖的瓶子里面装着一些水(如图)，由图中的数据 3.14π可推知瓶子的容积是_______ 立方厘米((取) Otherwise the pump should be checked again to install. 4.2.5.1 structure embedded phase 1, toilet drain structure places a waterproof steel bushings, measure width of the beam, use galvanized steel pipe welding and sealing rings, measure elevation on positions in the structure main bars of beams, welded prison using sawdust block. Hole thin iron sleeve construction, length about 200 mm, easy installation and handle construction, casing used touch Remover (available used oil paint), Eachd8, transfer and underground drainage pipe installation mounting, hang-dry pipe must first make an outline, the carrier according to the design of slope planted well hung code, pipe hangers, prefabricated piping Bay and state provision and other sanitary and drainage provision for finding sizes, clamp the connection interface. The connection between the pipe and the main pipe to ensure smooth, sloping according to design requirements, no camber behavior occurs. Buried trunk pipe supporting frame, before you install DUN, planted well pipe sizes, will be reserved for finding and fixed the pipe size, and then sealing with cement mortar. 9, after the construction of water testing, water testing and well outside through-ball after completion of construction. 10, construction notes: when using metal pipe clamps, 1086 4 (单位:厘米) 26.4π【巩固】一个酒精瓶，它的瓶身呈圆柱形(不包括瓶颈)，如图(已知它的容积为立方厘米(当瓶子正放时，瓶内的酒精的液面高为6厘米;瓶子倒放时，空余部分的高为2厘米(问:瓶内酒精的体积是多少立方厘米,合多少升, 2 6 30cm10cm15cm【巩固】一个酒瓶里面深，底面内直径是，瓶里酒深(把酒瓶塞紧后使其瓶口向下倒立这时 25cm酒深(酒瓶的容积是多少,(取3) π 30 25 15 10【巩固】一个盖着瓶盖的瓶子里面装着一些水，瓶底面积为平方厘米，(如下图所示)，请你根据图中标明的数据，计算瓶子的容积是,,,,,,( 7cm5cm 4cm 【巩固】一个透明的封闭盛水容器，由一个圆柱体和一个圆锥体组成，圆柱体的底面直径和高都是12厘米(其内有一些水，正放时水面离容器顶厘米，倒放时水面离顶部5厘米，那么这个容器的容积是多少11 π,3立方厘米,() 5cm11cm 4xed the pipe size, and then sealing with cement mortar. 9, after the construction of water testing, water testing and well ouball after completion of construction. 10, construction notes: when using metal pipe clamps,-throughtside urs. Buried trunk pipe supporting frame, before you install DUN, planted well pipe sizes, will be reserved for finding and fior ocche connection between the pipe and the main pipe to ensure smooth, sloping according to design requirements, no camber behavipiping Bay and state provision and other sanitary and drainage provision for finding sizes, clamp the connection interface. Tbricated dry pipe must first make an outline, the carrier according to the design of slope planted well hung code, pipe hangers, prefa-used touch Remover (available used oil paint), Eachd8, transfer and underground drainage pipe installation mounting, hangasing on using sawdust block. Hole thin iron sleeve construction, length about 200 mm, easy installation and handle construction, cvanized steel pipe welding and sealing rings, measure elevation on positions in the structure main bars of beams, welded pristerproof steel bushings, measure width of the beam, use galOtherwise the pump should be checked again to install. 4.2.5.1 structure embedded phase 1, toilet drain structure places a wa |初一?数学?基础-提高-精英?学生版| 第1讲 第页 【例 11】 (第四届希望杯2试试题)如图，底面积为50平方厘米的圆柱形容器中装有水，水面上漂浮着一 块棱长为5厘米的正方体木块，木块浮出水面的高度是2厘米(若将木块从容器中取出，水面将下 降________厘米( 2厘米 88【例 12】 有两个棱长为厘米的正方体盒子，盒中放入直径为厘米、高为8厘米的圆柱体铁块一个，A 盒中放入直径为4厘米、高为8厘米的圆柱体铁块4个，现在盒注满水，把盒的水倒入盒，BAAB 使盒也注满水，问盒余下的水是多少立方厘米, BA 【例 13】 兰州来的马师傅擅长做拉面，拉出的面条很细很细，他每次做拉面的步骤是这样的:将一个面 1.61.61.6团先搓成圆柱形面棍，长米(然后对折，拉长到米;再对折，拉长到米……照此继续进 1行下去，最后拉出的面条粗细(直径)仅有原先面棍的(问:最后马师傅拉出的这些细面条的总长64 有多少米,(假设马师傅拉面的过程中(面条始终保持为粗细均匀的圆柱形，而且没有任何浪费) 【例 14】 一个圆柱形容器内放有一个长方形铁块,现打开水龙头往容器中灌水,3分钟时水面恰好没过 长方体的顶面,再过18分钟水灌满容器,已知容器的高为50厘米,长方体的高为20厘米,求长方 体底面面积与容器底面面积之比, 15【例 15】 一只装有水的圆柱形玻璃杯，底面积是80平方厘米，高是厘米，水深8厘米(现将一个底 面积是16平方厘米，高为厘米的长方体铁块竖放在水中后(现在水深多少厘米, 12 1510【巩固】一只装有水的圆柱形玻璃杯，底面积是80平方厘米，高是厘米，水深厘米(现将一个底面积 是16平方厘米，高为厘米的长方体铁块竖放在水中后(现在水深多少厘米, 12 Otherwise the pump should be checked again to install. 4.2.5.1 structure embedded phase 1, toilet drain structure places a waterproof steel bushings, measure width of the beam, use galvanized steel pipe welding and sealing rings, measure elevation on positions in the structure main bars of beams, welded prison using sawdust block. Hole thin iron sleeve construction, length about 200 mm, easy installation and handle construction, casing used touch Remover (available used oil paint), Eachd8, transfer and underground drainage pipe installation mounting, hang-dry pipe must first make an outline, the carrier according to the design of slope planted well hung code, pipe hangers, prefabricated piping Bay and state provision and other sanitary and drainage provision for finding sizes, clamp the connection interface. The connection between the pipe and the main pipe to ensure smooth, sloping according to design requirements, no camber behavior occurs. Buried trunk pipe supporting frame, before you install DUN, planted well pipe sizes, will be reserved for finding and fixed the pipe size, and then sealing with cement mortar. 9, after the construction of water testing, water testing and well outside through-ball after completion of construction. 10, construction notes: when using metal pipe clamps, 1513【巩固】一只装有水的圆柱形玻璃杯，底面积是80平方厘米，高是厘米，水深厘米(现将一个底面积 厘米的长方体铁块竖放在水中后(现在水深多少厘米, 是16平方厘米，高为12 2.5【例 16】 一个圆柱形玻璃杯内盛有水,水面高厘米,玻璃杯内侧的底面积是72平方厘米,在这个杯 中放进棱长6厘米的正方体铁块后,水面没有淹没铁块,这时水面高多少厘米？ 【例 17】 一个盛有水的圆柱形容器,底面内半径为5厘米,深20厘米,水深15厘米,今将一个底面半 径为2厘米,高为17厘米的铁圆柱垂直放入容器中,求这时容器的水深是多少厘米？ 【例 18】 有甲、乙两只圆柱形玻璃杯,其内直径依次是10厘米、20厘米,杯中盛有适量的水,甲杯中 沉没着一铁块,当取出此铁块后,甲杯中的水位下降了2厘米;然后将铁块沉没于乙杯,且乙杯中 的水未外溢,问:这时乙杯中的水位上升了多少厘米？ 【巩固】有一只底面半径是20厘米的圆柱形水桶,里面有一段半径是5厘米的圆柱体钢材浸在水中,钢材从 水桶里取出后,桶里的水下降了6厘米,这段钢材有多长？ 6ball after completion of construction. 10, construction notes: when using metal pipe clamps,-throughtside xed the pipe size, and then sealing with cement mortar. 9, after the construction of water testing, water testing and well ouurs. Buried trunk pipe supporting frame, before you install DUN, planted well pipe sizes, will be reserved for finding and fior ocche connection between the pipe and the main pipe to ensure smooth, sloping according to design requirements, no camber behaviOtherwise the pump should be checked again to install. 4.2.5.1 structure embedded phase 1, toilet drain structure places a wapiping Bay and state provision and other sanitary and drainage provision for finding sizes, clamp the connection interface. Tbricated dry pipe must first make an outline, the carrier according to the design of slope planted well hung code, pipe hangers, prefa-used touch Remover (available used oil paint), Eachd8, transfer and underground drainage pipe installation mounting, hangasing on using sawdust block. Hole thin iron sleeve construction, length about 200 mm, easy installation and handle construction, cvanized steel pipe welding and sealing rings, measure elevation on positions in the structure main bars of beams, welded pristerproof steel bushings, measure width of the beam, use gal |初一?数学?基础-提高-精英?学生版| 第1讲 第页 【例 19】 一个圆锥形容器高24厘米，其中装满水，如果把这些水倒入和圆锥底面直径相等的圆柱形容器 中，水面高多少厘米, 【例 20】 (2009年”希望杯”一试六年级)如图，圆锥形容器中装有水50升，水面高度是圆锥高度的一 半，这个容器最多能装水 升( r 1r2h 1h2 12【例 21】 如图，甲、乙两容器相同，甲容器中水的高度是锥高的，乙容器中水的高度是锥高的，比33 较甲、乙两容器，哪一只容器中盛的水多,多的是少的的几倍, 乙 甲 【例 22】 (2008年仁华考题)如图，有一卷紧紧缠绕在一起的塑料薄膜，薄膜的直径为20厘米，中间有一 0.04直径为8厘米的卷轴，已知薄膜的厚度为厘米，则薄膜展开后的面积是 平方米( 8cm20cm 100cm 0.4【巩固】图为一卷紧绕成的牛皮纸,纸卷直径为20厘米,中间有一直径为6厘米的卷轴,已知纸的厚度为 毫米,问:这卷纸展开后大约有多长？ 0.25【巩固】如图，厚度为毫米的铜版纸被卷成一个空心圆柱(纸卷得很紧，没有空隙)，它的外直径是180Otherwise the pump should be checked again to install. 4.2.5.1 structure embedded phase 1, toilet drain structure places a waterproof steel bushings, measure width of the beam, use galvanized steel pipe welding and sealing rings, measure elevation on positions in the structure main bars of beams, welded prison using sawdust block. Hole thin iron sleeve construction, length about 200 mm, easy installation and handle construction, casing used touch Remover (available used oil paint), Eachd8, transfer and underground drainage pipe installation mounting, hang-dry pipe must first make an outline, the carrier according to the design of slope planted well hung code, pipe hangers, prefabricated piping Bay and state provision and other sanitary and drainage provision for finding sizes, clamp the connection interface. The connection between the pipe and the main pipe to ensure smooth, sloping according to design requirements, no camber behavior occurs. Buried trunk pipe supporting frame, before you install DUN, planted well pipe sizes, will be reserved for finding and fixed the pipe size, and then sealing with cement mortar. 9, after the construction of water testing, water testing and well outside through-ball after completion of construction. 10, construction notes: when using metal pipe clamps, 厘米，内直径是50厘米(这卷铜版纸的总长是多少米, 人大附中分班考试题目)如图，在一个正方体的两对侧面的中心各打通一个长方体的洞，在上【例 23】 ( 下底面的中心打通一个圆柱形的洞(已知正方体边长为10厘米，侧面上的洞口是边长为4厘米的正方形，上下底面的洞口是直径为4厘米的圆，求此立体图形的表面积和体积( 板块二 旋转问题 ABCACAC,ABC,ABC【例 24】 如图，是直角三角形，、的长分别是3和4(将绕旋转一周，求AB π,3.14扫出的立体图形的体积(() C AB 3cm4cm5cm【例 25】 已知直角三角形的三条边长分别为，，，分别以这三边轴，旋转一周，所形成的 3.14立体图形中，体积最小的是多少立方厘米,(取) π BC16πAC【巩固】如图，直角三角形如果以边为轴旋转一周，那么所形成的圆锥的体积为，以边为轴旋转 12π一周，那么所形成的圆锥的体积为，那么如果以为轴旋转一周，那么所形成的几何体的体积AB 是多少, B AC 8ball after completion of construction. 10, construction notes: when using metal pipe clamps,-throughtside xed the pipe size, and then sealing with cement mortar. 9, after the construction of water testing, water testing and well ouurs. Buried trunk pipe supporting frame, before you install DUN, planted well pipe sizes, will be reserved for finding and fior ocche connection between the pipe and the main pipe to ensure smooth, sloping according to design requirements, no camber behaviOtherwise the pump should be checked again to install. 4.2.5.1 structure embedded phase 1, toilet drain structure places a wapiping Bay and state provision and other sanitary and drainage provision for finding sizes, clamp the connection interface. Tbricated dry pipe must first make an outline, the carrier according to the design of slope planted well hung code, pipe hangers, prefa-used touch Remover (available used oil paint), Eachd8, transfer and underground drainage pipe installation mounting, hangasing on using sawdust block. Hole thin iron sleeve construction, length about 200 mm, easy installation and handle construction, cvanized steel pipe welding and sealing rings, measure elevation on positions in the structure main bars of beams, welded pristerproof steel bushings, measure width of the beam, use gal |初一?数学?基础-提高-精英?学生版| 第1讲 第页 【例 26】 如图，ABCD是矩形，BC,6cm，AB,10cm，对角线AC、相交O(、分别是与BDEFAD BC的中点，图中的阴影部分以为轴旋转一周，则白色部分扫出的立体图形的体积是多少立方厘EF 米,(取3) π EDA O CBF ABCDBC,6cmAB,10cmAC【巩固】(2006年第十一届华杯赛决赛试题)如图，是矩形，，，对角线、BD OCD相交(图中的阴影部分以为轴旋转一周，则阴影部分扫出的立体的体积是多少立方厘米, AD O BC Otherwise the pump should be checked again to install. 4.2.5.1 structure embedded phase 1, toilet drain structure places a waterproof steel bushings, measure width of the beam, use galvanized steel pipe welding and sealing rings, measure elevation on positions in the structure main bars of beams, welded prison using sawdust block. Hole thin iron sleeve construction, length about 200 mm, easy installation and handle construction, casing used touch Remover (available used oil paint), Eachd8, transfer and underground drainage pipe installation mounting, hang-dry pipe must first make an outline, the carrier according to the design of slope planted well hung code, pipe hangers, prefabricated piping Bay and state provision and other sanitary and drainage provision for finding sizes, clamp the connection interface. The connection between the pipe and the main pipe to ensure smooth, sloping according to design requirements, no camber behavior occurs. Buried trunk pipe supporting frame, before you install DUN, planted well pipe sizes, will be reserved for finding and fixed the pipe size, and then sealing with cement mortar. 9, after the construction of water testing, water testing and well outside through-ball after completion of construction. 10, construction notes: when using metal pipe clamps,