名校
解题方法
1 . 古希腊哲学家发现并证明了只存在5种正多面体,即正四面体、正六面体、正八面体、正十二面体、正二十面体,其中正八面体是由8个等边三角形构成.正八面体在计算机科学中用于三维模型和场景的构建,以及人工智能领域中用于图象识别和处理,另外在晶体和材料科学中也被广泛应用.现有一个棱长为2的正八面体
,如图所示,下列说法中正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73cbd9eb22f75ad5304d8491b314a9a9.png)
A.若点![]() ![]() |
B.若该正八面体的12条棱中点在同一个球的球面上,则该球的表面积为![]() |
C.该正八面体内任意一点到8个侧面的距离之和为定值 |
D.已知正方体![]() ![]() |
您最近一年使用:0次
2024-06-11更新
|
351次组卷
|
2卷引用:河北省沧州市沧县中学2023-2024学年高三下学期模拟预测数学试题
名校
解题方法
2 . 已知矩形
,其中
,
,点D沿着对角线
进行翻折,形成三棱锥
,如图所示,则下列说法正确的是__________ (填写序号即可).
①点D在翻折过程中存在
的情况;
②三棱锥
可以四个面都是直角三角形;
③点D在翻折过程中,三棱锥
的表面积不变;
④点D在翻折过程中,三棱锥
的外接球的体积不变.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54275b7e571660d0a9e0370fbfe5050b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc11331a7b2d2619b40ee6d34c3bd620.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c586b72a984e1fd9082b9f02ef7f3e91.png)
①点D在翻折过程中存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc9aabd9a42a97a1108149fafca8a919.png)
②三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c586b72a984e1fd9082b9f02ef7f3e91.png)
③点D在翻折过程中,三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c586b72a984e1fd9082b9f02ef7f3e91.png)
④点D在翻折过程中,三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c586b72a984e1fd9082b9f02ef7f3e91.png)
您最近一年使用:0次
2024-06-10更新
|
457次组卷
|
2卷引用:黑龙江省2024届高三信息押题卷(四)数学试卷
2024·全国·模拟预测
3 . 如图1,一圆形纸片的圆心为
,半径为
,以
为中心作正六边形
,以正六边形的各边为底边作等腰三角形,使其顶角的顶点恰好落在圆
上,现沿等腰三角形的腰和中位线裁剪,裁剪后的图形如图2所示,将该图形以正六边形的边为折痕将等腰梯形折起,使得相邻的腰重合得到正六棱台.若该正六棱台的高为
,则其外接球的表面积为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41322821ce31416fdac8dd6e0aa41c71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35361e76a7c85d1886728c8d0200b234.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
4 . 已知八面体
由两个正四棱锥
和
组成.若该八面体的外接球半径为3,且平面
平面
,则该八面体的体积为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73cbd9eb22f75ad5304d8491b314a9a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55c6caa0455442437177ab9b995df37b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
A.28 | B.32 | C.36 | D.40 |
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解题方法
5 . 正方体
中,
,P在正方形
内(包括边界),下列结论正确的有( )
![](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/e168672b47d7e64dc1b404f8882c7dcf.png)
A.若![]() ![]() |
B.三棱锥![]() ![]() |
C.若Q为正方形![]() ![]() ![]() |
D.![]() |
您最近一年使用:0次
2024-06-02更新
|
637次组卷
|
3卷引用:湖北省宜荆荆随恩2024届高三5月联考(二模)数学试题
解题方法
6 . 已知圆台
的上下底面半径分别为1,2,高为
,
为下底面圆
的一条直径,
为上底面圆
的一条弦,且
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e65ac334119ccd6204402a7aba29a55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c4f6f74444b2b7947fc6e35c8d62322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70c0ebe1c0688a33afe02a2e31e14175.png)
A.圆台的体积为![]() |
B.圆台的母线与下底面所成角为![]() |
C.当![]() ![]() ![]() ![]() ![]() ![]() |
D.![]() ![]() |
您最近一年使用:0次
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7 . 已知四面体
的顶点
,
,
,
均在球
的球面上,
是边长为2的等边三角形,
,棱
,
,
的中点分别为
,
,
,过
,
,
三点的平面截四面体所得截面四边形的对角线互相垂直,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac451db3443cabb204f96c31fd4a02e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cbab4a3f9636fe3eeee75ba79d08a52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
A.![]() |
B.![]() ![]() |
C.直线![]() ![]() |
D.球![]() ![]() |
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名校
解题方法
8 . 正方体
的棱长为
,
是正方体表面及其内部一点,下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
A.若![]() ![]() ![]() |
B.若![]() ![]() ![]() ![]() |
C.若![]() ![]() ![]() |
D.若![]() ![]() |
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9 . 用两个平行平面去截球体,把球体夹在两截面之间的部分称为球台.根据祖暅原理(“幂势既同,则积不容异”),推导出球台的体积
,其中
分别是两个平行平面截球所得截面圆的半径,
是两个平行平面之间的距离.已知圆台
的上、下底面的圆周都在球
的球面上,圆台
的母线与底面所成的角为
,若圆台
上、下底面截球
所得的球台的体积比圆台
的体积大
,则球O的表面积
与圆台
的侧面积
的比值
的取值范围为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cbb6f33f82a6e40c2b76d950d7e318a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff8543261a8e351eb95cdfebb001a3b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eabd5f3a86afe49dcd70571e2b96cfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e65ac334119ccd6204402a7aba29a55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e65ac334119ccd6204402a7aba29a55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e65ac334119ccd6204402a7aba29a55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e95a79288fcb7e47fba4410722e2bc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e65ac334119ccd6204402a7aba29a55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/235f0a6fb218d28383e6f27f2df1f50f.png)
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10 . 已知圆锥
为底面圆心
的轴截面是面积为1的等腰直角三角形,
是底面圆周上的一个动点,直线
满足
,设直线
与
所成的角为
,直线
与
所成的角为
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/084baf3d1ad539acc1e0002d1fc3e163.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ed8f34be15c3cc76705f1045b1a7e63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/602d0265aa2b89076b0cff90853f7cfa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/602d0265aa2b89076b0cff90853f7cfa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
A.![]() ![]() | B.该圆锥内切球的表面积为![]() |
C.![]() ![]() | D.![]() |
您最近一年使用:0次