1 . 已知正方体
表面积为S,体积为V,从该正方体中切割出一个四面体
,其表面积
,体积为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9047cefc91e5ffe044761734a2cfe6c.png)
________ ,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/286a397daaee20664f1bc0acb86af07e.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bd773ebc2e951d18c15a2773e783231.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4764374bd2fb78e59cd0b283637baeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9047cefc91e5ffe044761734a2cfe6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/286a397daaee20664f1bc0acb86af07e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/15/b6f8acdc-0e4d-4f94-a05f-c478f9662a45.png?resizew=171)
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2023高三·全国·专题练习
2 . 已知直三棱柱
中,侧面
为正方形,AB=BC=2,且
,E,F分别为AC和
的中点.则四棱锥
的侧面积为______ ;三棱锥
的体积为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9edc50f7febbc2d5d8dcdc23a3630a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f62f79e2b6bbb509b60d6ae830b5eb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83661ebf0bbfb0b0db0ca079f16f9763.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/7/c0df14e9-7d29-40c9-8fa7-5c97cac1b844.png?resizew=152)
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解题方法
3 . 设
是空间中两两夹角都为
的三条数轴,
分别是与
轴正方向同向的单位向量,若
,则把有序数对
叫作向量
在坐标系
中的坐标.
(1)若
,且
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edff1881635893293dd411ead8194aca.png)
__________ ;
(2)若
,则三棱锥
的表面积为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1b53cb1302f163699ecbefb7e90fd1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9437b3e173e4c3efc97bfb4df79c1b5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a14c388e1e2e5a2ff1ccf6caffbee0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b2839bbff6b2b33bcf496d36eba548e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f56ffc3672f2aee744a186796c26f2cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91174b2336306191ba275a87864172b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5e336d6ca2cae3d6e6c3810d7e521a4.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3f82202deaac4d6250bade5bc03eb15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13405345d862b41fee3412740c58ba19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edff1881635893293dd411ead8194aca.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c710792a0f4f63a9b140c9b61f3ae5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4278c0911e7df78965e78cff69cac5f5.png)
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2023-02-14更新
|
80次组卷
|
2卷引用:陕西省西北农林科技大学附属中学2022-2023学年高二上学期期末理科数学试题
4 . 已知菱形ABCD中,
,
,现将此菱形沿对角线BD对折,在折的过程中,当三棱锥
体积最大时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae248960d8c1677cf948f8251275e863.png)
______ ;当三棱锥
表面积最大时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae248960d8c1677cf948f8251275e863.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5b8b98b2f83279a49e94d9f48c5e6f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d42e97eee705d164e6ac6de9ecd6d1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3931333820859378ea6723ff3075189.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae248960d8c1677cf948f8251275e863.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3931333820859378ea6723ff3075189.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae248960d8c1677cf948f8251275e863.png)
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5 . 如图,一个正三棱锥的顶点是圆柱上底面的圆心,正三棱锥的底面是圆柱下底面的内接正三角形(这样的正三棱锥叫做圆柱的内接正三棱锥).如果在这个圆柱体中挖去这个正三棱锥得到的几何体如图所示,按图中所给尺寸所得几何体的表面积为______ ,体积为______ .
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/17/f87bc1b6-50e9-4d5e-b0dc-5fce6c3787d0.png?resizew=168)
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6 . 在棱长为1的正方体
中,P为正方体内一动点(包括表面),若
,且
.则点P所有可能的位置所构成的几何体的体积是________ ;表面积是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b145dc4f234a502249c72228fbe3dfdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/184bdabcc83fb710ad7fab7fbea77065.png)
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7 . 如图,在正方体
中,
,则四棱锥
的表面积为___________ ;若该正方体的顶点都在球O的球面上,则球O的体积为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbdf831e53dd9c7227bce030bdcd84b9.png)
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名校
8 . 已知一个底面边长为
,侧棱长为3的正三棱锥,则此三棱锥的侧面与底面所成三面角的余弦值为___________ ,此三棱锥内切球的半径为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
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解题方法
9 . 某几何体的三视图如图所示,则该几何体的体积为________ ,表面积为________ .
![](https://img.xkw.com/dksih/QBM/2022/4/29/2968550020440064/2972047983452160/STEM/1e330a11-17fc-4660-868f-e9a34d18b914.png?resizew=253)
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名校
解题方法
10 . 在四棱锥
中,PA⊥平面ABCD,四边形ABCD是边长为1的正方形,且
,则四棱锥
的表面积是___ ,四棱锥
外接球的体积是___ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b80ee363635d73f601654339028daec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
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2022-03-15更新
|
400次组卷
|
2卷引用:湖南省常德市临澧县第一中学2021-2022学年高三下学期第九次阶段性考试数学试题