1 . 如图,在几何体
中,
,
,
,侧棱
,
,
均垂直于底面
,
,
,
,求该几何体的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce31be11fffb48404921f7ff10b771fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e62676bcf5f9783c0457fce09fe561a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98bed2b2f5840b15af5c25bf9ed8a6c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1682d306c38087d9e6f7efb9cec596a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32f01c4faacedfe56f5127d6c0cc63cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c99bcc3259fe9f24a8f2354b5534451.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c10dc340e7c5a270875fcea4d3ee8873.png)
![](https://img.xkw.com/dksih/QBM/2021/12/19/2876152827904000/2925268971864064/STEM/2949a543-2790-4aed-8a68-827545dc6ac8.png?resizew=198)
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2022-02-27更新
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990次组卷
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6卷引用:人教A版(2019) 必修第二册 突围者 第八章 第三节 课时1 棱柱、棱锥、棱台的表面积和体积
人教A版(2019) 必修第二册 突围者 第八章 第三节 课时1 棱柱、棱锥、棱台的表面积和体积内蒙古阿拉善盟第一中学2020-2021学年高二上学期第二次段考理科数学试题人教A版(2019) 必修第二册 实战演练 第八章 课时练习22 棱柱、棱锥、棱台的表面积和体积(已下线)8.3简单几何体的表面积和体积(第1课时)(导学案)原卷版-2021-2022学年高一数学同步备课 (人教A版2019 必修第二册)(已下线)第24讲 棱柱、棱锥、棱台的表面积和体积1(已下线)第八章立体几何初步知识1
名校
解题方法
2 . 如图,已知多面体
中,
,
,
均垂直于平面
.
,
,
,
.
![](https://img.xkw.com/dksih/QBM/2021/9/24/2815048579457024/2815220150419456/STEM/9ef861cc-ef82-4047-b39d-7e4210154f4a.png?resizew=206)
(I)证明:
平面
;
(II)求多面体
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a696a182fff038a86b2bbe8ca099442.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1859959fdb4c5edd8056893f94a10a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53e97fcdcfd6183b976a61ef3222c607.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e918b70b02a73685e3c536c7f380e2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1880586c33da315e49ccb6e2d531c6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81a2749f3f4224a1753bcbe2e13b88fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edaef4d07ca8645539b455e196a305d6.png)
![](https://img.xkw.com/dksih/QBM/2021/9/24/2815048579457024/2815220150419456/STEM/9ef861cc-ef82-4047-b39d-7e4210154f4a.png?resizew=206)
(I)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1068ada1763c76ec2121dfa32bf0fe38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b16cff607cdc2d69afc70dc778acbb.png)
(II)求多面体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
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2021-09-24更新
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4卷引用:黑龙江省哈尔滨市第三中学校2020-2021学年高二9月阶段性测试数学(文)试题
解题方法
3 . 已知某组合体的三视图如图所示.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/3/20c74a25-6b17-4301-96ce-8540eb995903.png?resizew=139)
(1)说明该几何体由那些简单几何体组成,并画出立体图形;
(2)求该几何体的表面积和体积.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/3/20c74a25-6b17-4301-96ce-8540eb995903.png?resizew=139)
(1)说明该几何体由那些简单几何体组成,并画出立体图形;
(2)求该几何体的表面积和体积.
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4 . 如图直角梯形
中,
,
,
,
,在梯形内挖去一个以
为半径的四分之一圆,图中阴影部分绕
所在直线旋转一周,求该旋转体的体积和表面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d439e428bc3bf8778c274dd683f4fde9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c986f2e9f9a728704184a7565548e46f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d4d00b86b2f067b902baf6e52f0faab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52705567101a48893de582656ef41527.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/833cfda415649b832cc136caed392753.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/828628c0876b45381c9a0edeb0fec236.png)
![](https://img.xkw.com/dksih/QBM/2021/10/12/2827551435243520/2845554496692224/STEM/d3725786d1af43119a6f88de49de6fb6.png?resizew=172)
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解题方法
5 . 一个几何体的三视图如图所示,则此几何体的体积为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/18/db52bbb2-df7d-438c-bc9e-ef729ceaeccb.png?resizew=171)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/18/db52bbb2-df7d-438c-bc9e-ef729ceaeccb.png?resizew=171)
A.![]() | B.![]() | C.![]() | D.![]() |
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2021-09-05更新
|
383次组卷
|
3卷引用:浙江省金丽衢十二校2020-2021学年高三上学期第一次联考数学试题
6 . 如图,在多面体ABCDEF中,四边形ABCD是菱形,∠ABC=60°,FA⊥平面ABCD,ED//FA,且AB=FA=2ED=2.
![](https://img.xkw.com/dksih/QBM/2022/1/6/2888534285066240/2890623850823680/STEM/f63e09383be8426cb10286258b6542ce.png?resizew=149)
(1)求证:平面FAC⊥平面EFC;
(2)求多面体ABCDEF的体积.
![](https://img.xkw.com/dksih/QBM/2022/1/6/2888534285066240/2890623850823680/STEM/f63e09383be8426cb10286258b6542ce.png?resizew=149)
(1)求证:平面FAC⊥平面EFC;
(2)求多面体ABCDEF的体积.
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2022-01-09更新
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9卷引用:【市级联考】山东省栖霞市2019届高三高考模拟卷(新课标I)数学(文)试题
【市级联考】山东省栖霞市2019届高三高考模拟卷(新课标I)数学(文)试题河北省衡水市2020届高三下学期3月第五次调研数学(文)试题(已下线)强化卷06(3月)-冲刺2020高考数学之少丢分题目强化卷(山东专版)山西省山西大学附属中学2019-2020学年高三下学期3月(总第十一次)模块诊断数学(文)试题(已下线)【新东方】杭州新东方高中数学试卷332(已下线)专题06几何体表面积体积与球切、接的问题(测)(文科)第一篇 热点、难点突破篇-《2022年高考文科数学二轮复习讲练测》(全国课标版)(已下线)专题06几何体表面积体积与球切、接的问题(测)(理科)第一篇 热点、难点突破篇-《2022年高考理科数学二轮复习讲练测》(全国课标版)陕西省安康中学本部和分校2021-2022学年高二上学期期末联考文科数学试题陕西省安康市安康中学本部和分校2021-2022学年高二上学期期末数学(文)试题
名校
解题方法
7 . 某几何体的三视图如图所示,则该几何体的体积为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/9/41a31e07-a95a-4cd9-9ea9-4188dbfc3421.jpg?resizew=173)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/9/41a31e07-a95a-4cd9-9ea9-4188dbfc3421.jpg?resizew=173)
A.![]() | B.![]() | C.![]() | D.![]() |
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2021-08-15更新
|
281次组卷
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2卷引用:河北省石家庄市藁城区第一中学2020届高三下学期月考二数学(理)试题
8 . 取棱长为
的正方体的一个顶点,过从此顶点出发的三条棱的中点作截面,依次进行下去,对正方体的所有顶点都如此操作,所得的各截面与正方体各面共同围成一个多面体,如图所示.则此多面体:
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/ee49f652-b1e3-408b-997a-8ce03ce04f93.png?resizew=142)
①有12个顶点;②有24条棱;③有12个面;
④表面积为
;⑤体积为
.
以上结论正确的是________ .(填上所有正确的序号)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/ee49f652-b1e3-408b-997a-8ce03ce04f93.png?resizew=142)
①有12个顶点;②有24条棱;③有12个面;
④表面积为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f6ddb3766b5215c115a0abf597598aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86d2041c3e82a8153971971d9bd8fd64.png)
以上结论正确的是
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9 . 如图,四边
为矩形,
平面
,
,
,
,
,则多面体
的体积等于______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7a38e6c6dfde2b19b6b47f35a439a06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f0bdcaedc3437c28acddc90eba002a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f8eeeea1c9652cacce976f8129cf520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5c280edd2352edd640ee192ab61c20c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/31/0620b564-0298-4dea-a03c-cd5243a02eb2.png?resizew=183)
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名校
解题方法
10 . 如图,在直角梯形
中,
,
,
,
.
平面
,
,
是
的中点.
![](https://img.xkw.com/dksih/QBM/2021/7/12/2762390284443648/2764081889214464/STEM/d8942415bc8a4cee988f59a4b4f70b02.png?resizew=164)
(1)求证:
平面
;
(2)若
,
,求多面体
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10df84d553a8826a7ce9bff4bf0d95b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cd6c45556e76af03be8b521396bed6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84e0b7d845cbceccd3e76ca461fcc534.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a36f7e5128bcf12583792fe8a4a4d8fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42685c851148cafa4c193c627c1b8484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/2021/7/12/2762390284443648/2764081889214464/STEM/d8942415bc8a4cee988f59a4b4f70b02.png?resizew=164)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d0492b25f10ae45c39f8e9838519259.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c66d99a6a8415ddad22bbed33b64cfb.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38c5c9cc1ed4bce98b7fae77e70b227f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf394a6f336510a2d3b998e5024304f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
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