名校
解题方法
1 . 如图,已知一个八面体的各条棱长均为
,四边形
为正方形,给出下列说法:
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/3e7487cf-8589-4c0e-b9f7-89f114f21294.png?resizew=162)
①该八面体的体积为
;
②该八面体的外接球的表面积为
;
③
到直线
的距离为
;
④
与
所成角为
.
其中正确的说法为___________ .(填序号)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/3e7487cf-8589-4c0e-b9f7-89f114f21294.png?resizew=162)
①该八面体的体积为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a391005600bdd69c96750589f9adb048.png)
②该八面体的外接球的表面积为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4986217611fc5eefe70fd217a9d5726a.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fc56c77464a17a1e97b568762a3e2c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
其中正确的说法为
您最近一年使用:0次
解题方法
2 . 已知边长为
的等边三角形
中,
、
分别为
、
边上的点,且
,将
沿
折成
,使平面
平面
,则几何体
的体积的最大值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d459cad63e3cd2aba10862800fa4832.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c105d6ba18fbb0581fb982175e2eac9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cde52e02168c74b4b1c0a8ce09287df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be202354cc5457916b91330b47b729e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a03952d664fba91020fc5f3bcf2f9746.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2eeacf2b3f89024386f181782e62bd7c.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
3 . 如图,正三棱锥(底面是正三角形,侧棱长都相等)
的底面边长为2,侧棱长为3.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/98fd992c-9188-4189-a276-291f04b41e51.png?resizew=155)
(1)求正三棱锥
的表面积;
(2)求正三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/98fd992c-9188-4189-a276-291f04b41e51.png?resizew=155)
(1)求正三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
(2)求正三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
您最近一年使用:0次
4 . 如图,三棱柱
,
底面
,且
为正三角形,
,
为
中点.
![](https://img.xkw.com/dksih/QBM/2016/2/26/1572502490578944/1572502496714752/STEM/44d70711-95e7-4da4-860d-e138f24cc6ba.png?resizew=157)
(1)求三棱锥
的体积;
(2)求证:平面
平面
;
(3)求证:直线
平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ccc0d735dc14c92a8926d9b1def6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/565517c781e119de8d8e9c9f29e4e2dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://img.xkw.com/dksih/QBM/2016/2/26/1572502490578944/1572502496714752/STEM/44d70711-95e7-4da4-860d-e138f24cc6ba.png?resizew=157)
(1)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd8579d3c939467a9db200c15a6a6f2c.png)
(2)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f7d9ac3c0e60f1419dc90a37ff731b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
(3)求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1c920d02068d0e63ffdab70786c526d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a935b7d21a103a264b6e96ecf82dbe4a.png)
您最近一年使用:0次
2016-12-04更新
|
1609次组卷
|
3卷引用:2015-2016学年安徽省涡阳四中等高一上学期期末数学试卷
解题方法
5 . 如图,四棱锥
中,
为正方形,平面
平面
.
![](https://img.xkw.com/dksih/QBM/2020/8/5/2521508015955968/2522278403244032/STEM/4d5c2ad4626e4cbaaf1a7c72a6c7688a.png?resizew=237)
(1)证明:
;
(2)若
,
,求四棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/2020/8/5/2521508015955968/2522278403244032/STEM/4d5c2ad4626e4cbaaf1a7c72a6c7688a.png?resizew=237)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c583493109d50c9e4634c05e9042a9f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b70e550fa3c5aaf1b9c28f36fd5ed5d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
您最近一年使用:0次
名校
6 . 四棱锥P﹣ABCD,底面为正方形ABCD,边长为4,E为AB中点,PE⊥平面ABCD.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/801b45aa-808d-4db9-b886-374a768bf257.png?resizew=179)
(1)若
为等边三角形,求四棱锥P﹣ABCD的体积;
(2)若CD的中点为F,PF与平面ABCD所成角为45°,求PC与AD所成角的正切值.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/801b45aa-808d-4db9-b886-374a768bf257.png?resizew=179)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
(2)若CD的中点为F,PF与平面ABCD所成角为45°,求PC与AD所成角的正切值.
您最近一年使用:0次
名校
解题方法
7 . 正方形
与梯形
所在平面互相垂直,
,
,
,
,点
是
中点 .
![](https://img.xkw.com/dksih/QBM/2017/12/27/1847529124732928/1848252063375360/STEM/2fd9d9a9b5874cfdb2d05e2870614884.png?resizew=302)
(1)求证:
平面
;
(2)求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ecc1cb55a57dde481f8dd07ab150676.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdb2dd10731b99c0f4f89ee957f8a239.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f79863ffcfa63117ca6741b20a48e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27db558e8db4c957654c8e5cecd2d2dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e673ef2d48215ca84a48377f17d6df00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fc56c77464a17a1e97b568762a3e2c6.png)
![](https://img.xkw.com/dksih/QBM/2017/12/27/1847529124732928/1848252063375360/STEM/2fd9d9a9b5874cfdb2d05e2870614884.png?resizew=302)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f369bec2d5682bf6b8b317a08aff546.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ecc1cb55a57dde481f8dd07ab150676.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee48b4d6b9ee347b2ba6305f2fdc2bb0.png)
您最近一年使用:0次
2017-12-28更新
|
798次组卷
|
9卷引用:【全国百强校】安徽亳州市涡阳一中2018届高三最后一卷数学(文)试题
【全国百强校】安徽亳州市涡阳一中2018届高三最后一卷数学(文)试题2015届吉林省实验中学高三年级第二次模拟考试文科数学试卷山东省烟台市实验中学2018届高三上学期第三次诊断考试文科数学试题山东省济南外国语学校2018届高三1月月考数学(文)试题【校级联考】广西南宁市马山县金伦中学“4+ N”高中联合体2018-2019学年高二上学期期中考试数学(文)试题西藏拉萨那曲第二高级中学2021届高三上学期第二次月考数学(文)试题西藏拉萨那曲第二高级中学2021届高三上学期第二次月考数学(理)试题甘肃省兰州市永登县第一中学2020-2021学年高三上学期期末数学(文)试题陕西省咸阳市高新一中2022-2023学年高三上学期第五次质量检测文科数学试题
解题方法
8 . 某几何体的三视图如图所示,体积为______ .
![](https://img.xkw.com/dksih/QBM/2020/11/9/2589446621626368/2592999865884672/STEM/948116c4b88c4e529c8f6efc2279f2a4.png?resizew=192)
您最近一年使用:0次
9 . 已知圆锥的底面半径为
,母线与底面所成的角为
,则此圆锥的侧面积为_____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d5bca00fa20e6e80480b9d06d2e52ee.png)
您最近一年使用:0次
名校
解题方法
10 . 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/2018/3/8/1897531248017408/1903538888433664/STEM/a4d9b89908074cef9ecdf812bb477420.png?resizew=161)
![](https://img.xkw.com/dksih/QBM/2018/3/8/1897531248017408/1903538888433664/STEM/a4d9b89908074cef9ecdf812bb477420.png?resizew=161)
A.![]() | B.![]() | C.![]() | D.1 |
您最近一年使用:0次
2018-03-16更新
|
478次组卷
|
5卷引用:【全国百强校】安徽亳州市涡阳一中2018届高三最后一卷数学(文)试题