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解题方法
1 . 如图,在正四棱台
中,
,
.若该四棱台的体积为
,则该四棱台的外接球表面积为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/570f8b295ee0c7c60e6fe1dbf054ff52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fa0d73f30a242947aaf7da525926266.png)
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2 . 如图,在棱长为
的正方体
中,点
在线段
上运动,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
A.平面![]() ![]() |
B.三棱锥![]() |
C.异面直线![]() ![]() ![]() |
D.当![]() ![]() ![]() ![]() |
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3 . 现为一球形玩具设计一款球形的外包装盒(盒子厚度忽略不计).已知该球形玩具的直径为2,每盒需放入4个玩具球,则该种外包装盒的直径的最小值为( )
A.![]() | B.![]() | C.![]() | D.![]() |
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4 . 在正方体
中,
,
为
的中点,
是正方形
内部一点(不含边界),则下列说法正确的是( )
![](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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c52091eb745de866044477641a7c55f.png)
A.平面![]() ![]() |
B.若直线![]() ![]() ![]() ![]() ![]() |
C.若四棱锥![]() ![]() ![]() ![]() |
D.以![]() ![]() ![]() ![]() ![]() ![]() |
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7日内更新
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2卷引用:江西省九师大联考2024届高三4月教学质量检测(二模)数学试题
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5 . 祖暅原理也称祖氏原理,是我国数学家祖暅提出的一个求体积的著名命题:“幂势既同,则积不容异”,“幂”是截面积,“势”是几何体的高,意思是两个同高的立体,如在等高处截面积相等,则体积相等.由曲线
,
,
围成的图形绕y轴旋转一周所得旋转体的体积为V,则V=__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c465114dc2665d74246240b1d4d26ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d63f162c4846a76cadee56ae2f42e37c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bfb4e91d5c6d50ff816b0240c1a7f02.png)
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2024-06-11更新
|
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5卷引用:江西省宜春市樟树中学2024届高三下学期高考数学仿真模拟试卷
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6 . 如图,将边长为1的正
以边
为轴逆时针翻转
弧度得到
,其中
,构成一个三棱锥
.若该三棱锥的外接球半径不超过
,则
的取值范围为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c430808cb91d66ce60b1e2f83f129db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/476c1028ab48d8f3779e1217b8bf63d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45bc09ca07b357a1ecf0c9588aa7030e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e5f1b9a7dc93aa2cd57d6352d000bb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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7 . 如图,已知正三棱锥
和正三棱锥
的侧棱长均为
.若将正三棱锥
绕
旋转,使得点
分别旋转至点
处,且
四点共面,点
分别位于
两侧,则下列说法中正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bf9718967af7a01c5b4866ea6f73bbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4f2d2ef6661d1808fed0cbd1b0fa53d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e13ba83790c5605647e39a560641061c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bf9718967af7a01c5b4866ea6f73bbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ff571c72c041d8668b4d2754679f64d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5de83ce4d5ad4bb47d74cbd3bc3394ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16e5d9f7e63d80a1969318ac999a3e6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e925a4d4d706168d1ae69167483096c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
A.多面体![]() | B.![]() |
C.![]() ![]() | D.点![]() ![]() |
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2024-05-29更新
|
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2卷引用:江西省南昌市第十九中学2024届高三下学期第四次模拟考试数学试卷
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8 . 下列物体,能够被整体放入长、宽、高分别为2,1,1(单位:m)的长方体容器(容器壁厚度忽略不计)内的有( )
A.半径为0.6m的球体 |
B.一组相对棱为1.4m,其余棱都为2m的四面体 |
C.底面半径为0.005m,高为2.5m的圆柱体 |
D.底面半径为0.6m,高为0.005m的圆柱体 |
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解题方法
9 . 在四棱锥
中,
是正方形,
,
,
,
为棱
上一点,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc904a45c77013665ccfbb58f72135d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdb64061e933aea7669294640c331bcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/add48f067e2ad2ab0a494c2eb071e3fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d4db9b82b67efe45a02fca32bfcf5dc.png)
A.点![]() ![]() |
B.若![]() ![]() ![]() ![]() ![]() ![]() |
C.四棱锥![]() ![]() |
D.直线![]() ![]() ![]() |
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10 . 在棱长为2的正方体
中,点E,F分别为棱
,
的中点,过点
的平面
与平面
平行,点
为线段
上的一点,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11875255224766f69d7fda20c2b12f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f66fb71b75b63594ebeeeebd1963eed5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bf9628142422a4884bd59538da6d312.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
A.![]() |
B.若点![]() ![]() ![]() ![]() |
C.底面半径为![]() ![]() ![]() |
D.直线![]() ![]() ![]() |
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|
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