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6．1.2　点、线、面、体
eq \o(\s\up7( INCLUDEPICTURE "知识梳理.tif" INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/知识梳理.tif" \* MERGEFORMAT INCLUDEPICTURE "../../知识梳理.tif" \* MERGEFORMAT INCLUDEPICTURE "../../知识梳理.tif" \* MERGEFORMAT INCLUDEPICTURE "../知识梳理.tif" \* MERGEFORMAT INCLUDEPICTURE "知识梳理.tif" \* MERGEFORMAT ),\s\do5(　　　　　　　))
知识点　点、线、面、体
点动成线，线动成面，面动成体．
练习　当你用笔在纸上画线时，你的笔尖实现了(　A　).
A．点动成线 B．线动成面
C．面动成体 D．以上都不对
总结　点、线、面、体的关系如下：
eq \o(\s\up7( INCLUDEPICTURE "课后练习.tif" INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/课后练习.tif" \* MERGEFORMAT INCLUDEPICTURE "../../课后练习.tif" \* MERGEFORMAT INCLUDEPICTURE "../../课后练习.tif" \* MERGEFORMAT INCLUDEPICTURE "../课后练习.tif" \* MERGEFORMAT INCLUDEPICTURE "课后练习.tif" \* MERGEFORMAT ),\s\do5(　　　　　　　))
INCLUDEPICTURE "三角.tif" INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/三角.tif" \* MERGEFORMAT INCLUDEPICTURE "../../三角.tif" \* MERGEFORMAT INCLUDEPICTURE "../../三角.tif" \* MERGEFORMAT INCLUDEPICTURE "../三角.tif" \* MERGEFORMAT INCLUDEPICTURE "三角.tif" \* MERGEFORMAT 基础巩固
1．将下方如图所示的直角梯形绕直线l旋转一周，得到的立体图形是(　D　).
INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/SX138.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX138.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX138.tif" \* MERGEFORMAT INCLUDEPICTURE "../SX138.tif" \* MERGEFORMAT INCLUDEPICTURE "SX138.tif" \* MERGEFORMAT
eq \o(\s\up7( INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/SX139.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX139.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX139.tif" \* MERGEFORMAT INCLUDEPICTURE "../SX139.tif" \* MERGEFORMAT INCLUDEPICTURE "SX139.tif" \* MERGEFORMAT ),\s\do5(A)) 　　 eq \o(\s\up7( INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/SX139A.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX139A.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX139A.tif" \* MERGEFORMAT INCLUDEPICTURE "../SX139A.tif" \* MERGEFORMAT INCLUDEPICTURE "SX139A.tif" \* MERGEFORMAT ),\s\do5(B)) 　　 eq \o(\s\up7( INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/SX139B.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX139B.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX139B.tif" \* MERGEFORMAT INCLUDEPICTURE "../SX139B.tif" \* MERGEFORMAT INCLUDEPICTURE "SX139B.tif" \* MERGEFORMAT ),\s\do5(C)) 　　 eq \o(\s\up7( INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/SX139C.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX139C.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX139C.tif" \* MERGEFORMAT INCLUDEPICTURE "../SX139C.tif" \* MERGEFORMAT INCLUDEPICTURE "SX139C.tif" \* MERGEFORMAT ),\s\do5(D))
2．如图所示的几何体是平面图形绕直线l旋转一周得到的，则该平面图形是(　D　).
INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/SX140.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX140.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX140.tif" \* MERGEFORMAT INCLUDEPICTURE "../SX140.tif" \* MERGEFORMAT INCLUDEPICTURE "SX140.tif" \* MERGEFORMAT
eq \o(\s\up7( INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/SX141.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX141.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX141.tif" \* MERGEFORMAT INCLUDEPICTURE "../SX141.tif" \* MERGEFORMAT INCLUDEPICTURE "SX141.tif" \* MERGEFORMAT ),\s\do5(A)) 　 eq \o(\s\up7( INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/SX141A.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX141A.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX141A.tif" \* MERGEFORMAT INCLUDEPICTURE "../SX141A.tif" \* MERGEFORMAT INCLUDEPICTURE "SX141A.tif" \* MERGEFORMAT ),\s\do5(B)) 　 eq \o(\s\up7( INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/SX141B.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX141B.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX141B.tif" \* MERGEFORMAT INCLUDEPICTURE "../SX141B.tif" \* MERGEFORMAT INCLUDEPICTURE "SX141B.tif" \* MERGEFORMAT ),\s\do5(C)) 　 eq \o(\s\up7( INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/SX141C.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX141C.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX141C.tif" \* MERGEFORMAT INCLUDEPICTURE "../SX141C.tif" \* MERGEFORMAT INCLUDEPICTURE "SX141C.tif" \* MERGEFORMAT ),\s\do5( D))
3．孙悟空的“金箍棒”飞速旋转，形成一个圆面，这说明________(填序号).
①点动成线；②线动成面；③面动成体．
【答案】②
4．如图，直角三角形绕它的一条直角边所在的直线旋转一周，形成的几何体是________，其中蕴含的数学事实是____________．
INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/SX143.TIF" \* MERGEFORMAT INCLUDEPICTURE "../../SX143.TIF" \* MERGEFORMAT INCLUDEPICTURE "../../SX143.TIF" \* MERGEFORMAT INCLUDEPICTURE "../SX143.TIF" \* MERGEFORMAT INCLUDEPICTURE "SX143.TIF" \* MERGEFORMAT
【答案】圆锥　面动成体
5．用一个平面去截以下几何体：①圆锥，②五棱柱，③圆柱，④三棱锥，⑤球，能得到截面是圆的几何体是________(填序号).
【答案】①③⑤
INCLUDEPICTURE "三角.tif" INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/三角.tif" \* MERGEFORMAT INCLUDEPICTURE "../../三角.tif" \* MERGEFORMAT INCLUDEPICTURE "../../三角.tif" \* MERGEFORMAT INCLUDEPICTURE "../三角.tif" \* MERGEFORMAT INCLUDEPICTURE "三角.tif" \* MERGEFORMAT 能力达标
6．小明用橡皮做了一个长方体，若用一把小刀去切该长方体，截面的形状不可能是(　A　).
A．圆 B．五边形
C．长方形 D．三角形
【解析】长方体共有六个面，故用平面截一个长方体时，最多与六个面都相交，此时截面为六边形，最少与三个面相交，此时截面为三角形，因此，截面的形状可能为三角形、四边形、五边形、六边形，不可能为圆．故选A.
7．分别以直角梯形(如图所示)的下底和上底为轴，将梯形旋转一周得到A，B两个立体图形，则A，B两个立体图形的体积比是(　C　).
INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/H5.tif" \* MERGEFORMAT INCLUDEPICTURE "../../H5.tif" \* MERGEFORMAT INCLUDEPICTURE "../../H5.tif" \* MERGEFORMAT INCLUDEPICTURE "../H5.tif" \* MERGEFORMAT INCLUDEPICTURE "H5.tif" \* MERGEFORMAT
INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/H5+.tif" \* MERGEFORMAT INCLUDEPICTURE "../../H5+.tif" \* MERGEFORMAT INCLUDEPICTURE "../../H5+.tif" \* MERGEFORMAT INCLUDEPICTURE "../H5+.tif" \* MERGEFORMAT INCLUDEPICTURE "H5+.tif" \* MERGEFORMAT
A．1∶1 B．1∶2
C．4∶5 D．5∶4
【解析】由题图，可知几何体A的体积为π×22×2＋π×22×(4－2)＝8π＋＝，几何体B的体积为π×22×4－π×22×(4－2)＝16π－π＝，所以几何体A与几何体B的体积比为4∶5.故选C.
8．如图所示，有一个长为4 cm、宽为3 cm的长方形．
INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/SX144.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX144.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX144.tif" \* MERGEFORMAT INCLUDEPICTURE "../SX144.tif" \* MERGEFORMAT INCLUDEPICTURE "SX144.tif" \* MERGEFORMAT
(1)若分别绕它们的相邻两边所在的直线旋转一周，会得到不同的几何体，请你画出这两个几何体；
(2)在你画出的这两个几何体中，哪个体积大？
【解】(1)如图所示即为所求．
INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/SX293.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX293.tif" \* MERGEFORMAT INCLUDEPICTURE "../../SX293.tif" \* MERGEFORMAT INCLUDEPICTURE "../SX293.tif" \* MERGEFORMAT INCLUDEPICTURE "SX293.tif" \* MERGEFORMAT
(2)绕4 cm长的边旋转一周所得圆柱体的体积＝π×32×4＝36π(cm3)；
绕3 cm长的边旋转一周所得圆柱体的体积＝π×42×3＝48π(cm3).
答：绕3 cm长的边旋转一周所得圆柱体的体积大．
INCLUDEPICTURE "三角.tif" INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/三角.tif" \* MERGEFORMAT INCLUDEPICTURE "../../三角.tif" \* MERGEFORMAT INCLUDEPICTURE "../../三角.tif" \* MERGEFORMAT INCLUDEPICTURE "../三角.tif" \* MERGEFORMAT INCLUDEPICTURE "三角.tif" \* MERGEFORMAT 挑战创新
9．下列说法正确的是(　C　).
eq \o(\s\up7( INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/H6.tif" \* MERGEFORMAT INCLUDEPICTURE "../../H6.tif" \* MERGEFORMAT INCLUDEPICTURE "../../H6.tif" \* MERGEFORMAT INCLUDEPICTURE "../H6.tif" \* MERGEFORMAT INCLUDEPICTURE "H6.tif" \* MERGEFORMAT ),\s\do5(图 甲)) 　 eq \o(\s\up7( INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/H6A.tif" \* MERGEFORMAT INCLUDEPICTURE "../../H6A.tif" \* MERGEFORMAT INCLUDEPICTURE "../../H6A.tif" \* MERGEFORMAT INCLUDEPICTURE "../H6A.tif" \* MERGEFORMAT INCLUDEPICTURE "H6A.tif" \* MERGEFORMAT ),\s\do5(图 乙)) 　 eq \o(\s\up7( INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/H6B.tif" \* MERGEFORMAT INCLUDEPICTURE "../../H6B.tif" \* MERGEFORMAT INCLUDEPICTURE "../../H6B.tif" \* MERGEFORMAT INCLUDEPICTURE "../H6B.tif" \* MERGEFORMAT INCLUDEPICTURE "H6B.tif" \* MERGEFORMAT ),\s\do5(图 丙))
eq \o(\s\up7( INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/H6C.tif" \* MERGEFORMAT INCLUDEPICTURE "../../H6C.tif" \* MERGEFORMAT INCLUDEPICTURE "../../H6C.tif" \* MERGEFORMAT INCLUDEPICTURE "../H6C.tif" \* MERGEFORMAT INCLUDEPICTURE "H6C.tif" \* MERGEFORMAT ),\s\do5(图 ①)) 　 eq \o(\s\up7( INCLUDEPICTURE "../../../../广东慧源同步上册/广东慧源七年级上册数学/H6D.tif" \* MERGEFORMAT INCLUDEPICTURE "../../H6D.tif" \* MERGEFORMAT INCLUDEPICTURE "../../H6D.tif" \* MERGEFORMAT INCLUDEPICTURE "../H6D.tif" \* MERGEFORMAT INCLUDEPICTURE "H6D.tif" \* MERGEFORMAT ),\s\do5(图 ②))
A．折叠图①，可得到图甲所示的正方体纸盒
B．图乙所示长方形绕它的对角线所在直线旋转一周，形成的几何体是图②
C．用一个平面去截图丙，截面图形可能是四边形
D．以上说法都不对6．1.2　点、线、面、体
eq \o(\s\up7(),\s\do5(　　　　　　　))
知识点　点、线、面、体
点动成线，线动成面，面动成体．
练习　当你用笔在纸上画线时，你的笔尖实现了(　).
A．点动成线 B．线动成面
C．面动成体 D．以上都不对
总结　点、线、面、体的关系如下：
eq \o(\s\up7(),\s\do5(　　　　　　　))
基础巩固
1．将下方如图所示的直角梯形绕直线l旋转一周，得到的立体图形是(　).
eq \o(\s\up7(),\s\do5( )) 　　 eq \o(\s\up7(),\s\do5( )) 　　 eq \o(\s\up7(),\s\do5( )) 　　 eq \o(\s\up7(),\s\do5( ))
2．如图所示的几何体是平面图形绕直线l旋转一周得到的，则该平面图形是(　).
eq \o(\s\up7(),\s\do5( )) 　 eq \o(\s\up7(),\s\do5( )) 　 eq \o(\s\up7(),\s\do5( )) 　 eq \o(\s\up7(),\s\do5( D))
3．孙悟空的“金箍棒”飞速旋转，形成一个圆面，这说明________(填序号).
①点动成线；②线动成面；③面动成体．
4．如图，直角三角形绕它的一条直角边所在的直线旋转一周，形成的几何体是________，其中蕴含的数学事实是____________．
5．用一个平面去截以下几何体：①圆锥，②五棱柱，③圆柱，④三棱锥，⑤球，能得到截面是圆的几何体是________(填序号).
、⑤
能力达标
6．小明用橡皮做了一个长方体，若用一把小刀去切该长方体，截面的形状不可能是(　).
A．圆 B．五边形
C．长方形 D．三角形
7．分别以直角梯形(如图所示)的下底和上底为轴，将梯形旋转一周得到A，B两个立体图形，则A，B两个立体图形的体积比是(　).
A．1∶1 B．1∶2
C．4∶5 D．5∶4
8．如图所示，有一个长为4 cm、宽为3 cm的长方形．
(1)若分别绕它们的相邻两边所在的直线旋转一周，会得到不同的几何体，请你画出这两个几何体；
(2)在你画出的这两个几何体中，哪个体积大？
挑战创新
9．下列说法正确的是(　).
eq \o(\s\up7(),\s\do5(图 甲)) 　 eq \o(\s\up7(),\s\do5(图 乙)) 　 eq \o(\s\up7(),\s\do5(图 丙))
eq \o(\s\up7(),\s\do5(图 ①)) 　 eq \o(\s\up7(),\s\do5(图 ②))
A．折叠图①，可得到图甲所示的正方体纸盒
B．图乙所示长方形绕它的对角线所在直线旋转一周，形成的几何体是图②
C．用一个平面去截图丙，截面图形可能是四边形
D．以上说法都不对

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