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解题方法
1 . 已知正四棱台的上底面与下底面的边长之比为
,其内切球的半径为1,则该正四棱台的体积为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37d65e051e943ab28fa57aee2fb57994.png)
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2024-06-04更新
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1561次组卷
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5卷引用:新疆乌鲁木齐市第二十三中学2023-2024学年高一下学期5月月考数学试题
新疆乌鲁木齐市第二十三中学2023-2024学年高一下学期5月月考数学试题湖北省武汉市2024届高三下学期5月模拟训练试题数学试卷(已下线)专题7 立体几何综合问题【练】(已下线)6.6.1-2 柱、锥、台的表面积和体积-同步精品课堂(北师大版2019必修第二册)(已下线)6.6.3 球的表面积和体积-同步精品课堂(北师大版2019必修第二册)
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2 . 体积为27的正方体的顶点都在同一球面上,则该球面的表面积为( )
A.![]() | B.![]() | C.![]() | D.![]() |
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3 . 下列命题错误的是( )
A.若A、B、C是平面内的三点,则![]() |
B.若![]() ![]() ![]() |
C.若![]() ![]() ![]() |
D.向量![]() ![]() |
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4 . 已知
,
,
,
,则向量
在向量
上的投影向量为______ (用坐标表示)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4212e0f2da912518e8b02a741cc91ad2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92a290a27cce9bd59bb6d79822473d8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9d6e498b0c1d1cedb86fe548f9fe79a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da0f23b0f0c453339d6db414305295d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abcb5d89b04570ceda2c29e11cb27a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc1070a28cb9cb8553c29747d1993b16.png)
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5 . 已知函数
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9127192aad98a69f269155fcab9e220.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99ea04abef07fcb0e53e5f51b4c1d6bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9127192aad98a69f269155fcab9e220.png)
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6 . 若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/009faf90dc1ad59216da4451c47c162a.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de8171f910574d5137b6cb90ebe99bea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/009faf90dc1ad59216da4451c47c162a.png)
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7 . 已知向量
,
,则向量
在向量
方向上的投影向量的坐标为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f29ea1d6fd62eef9100aec3b839beea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32cde768af0b6520211805e04decb739.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94075193c11fe43f2396cff5a485054.png)
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8 . 已知数列
的首项
,且
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d5a99603dd831f8b3612245fa2303f5.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05d4f2dc952ce53ed4bd6f56f3aa6ffa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d5a99603dd831f8b3612245fa2303f5.png)
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9 . 下列各式正确的个数为( )
①
;②
;③
;④
.
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03d16126c03f73e5386449272ec02fad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55500138470e2723ec75ba96cc3e6e66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f92a434f34942c460ed6b4a96e04317f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c5143af7f667df0c191fd70741194f4.png)
A.1 | B.2 | C.3 | D.4 |
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10 . (1)化简下列各式:
①
;
②
.
(2)已知向量
,
,
与
的夹角为
.
①求
;
②求
.
(3)已知向量
,
.
①求
;
②若
,求实数
的值.
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4074b93ead6f32e784576801e5193c00.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4bb22718194f581c971f54e7bc2e77a.png)
(2)已知向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29276b43a2950ed71f0f9629a35dfa74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2396cac4b185cf1f1a67dad9248481c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1a63ab608517bb10aa036783dfb51f.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/854e16eb319ee454088f5b527cf6c4d5.png)
②求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93af88a7628c71d642d3a6df067c15f5.png)
(3)已知向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5463fb0b7d03747aa4d680620ca81be2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aabefecd4de8455e21919d34005588f.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08e6f98f23fea7db0f74897928024ca0.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25d209e529faa74004ca556cf3d6b321.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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