名校
1 . 如图,已知
平面ABC,
,
,
,
,
,点
为
的中点
平面
;
(2)求直线
与平面
所成角的大小;
(3)若点
为
的中点,求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ccc0d735dc14c92a8926d9b1def6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa742d9b84b537be10034553776400e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e4f0c1c9cca0555906d8a53e1a6803d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/133760237c0ccf2d6a83786925b6d23c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ab527e1b5f124429b532804ef3f870f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4eaac4ba87386eca79a4f8b5d99ec38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f4c3f9dd5d0343597a7f58a1989b537.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb7f072f0834ebdf155abc5dcc9c8d99.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb7f072f0834ebdf155abc5dcc9c8d99.png)
(3)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
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昨日更新
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698次组卷
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4卷引用:福建省安溪第一中学2023-2024学年高一下学期5月份质量检测数学试题
福建省安溪第一中学2023-2024学年高一下学期5月份质量检测数学试题吉林省长春外国语学校2023-2024学年高一下学期5月期中考试数学试题四川省凉山州宁南中学2023-2024学年高一下学期数学期末复习卷二(已下线)专题2 以立体几何为背景的各类证明和计算问题【讲】(高一期末压轴专项)
2 . 如图,已知
为圆锥
的底面的直径,
,C为底面圆周上一点,弧
的长度是弧
的长度的2倍,异面直线
与
所成角的余弦值为
,则( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18e5ef91fb27dd684a27ae7f1993cfba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1804c3641953c30ccf750504eff6577.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d4db9b82b67efe45a02fca32bfcf5dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56d266a04f3dc7483eddbc26c5e487db.png)
A.圆锥![]() ![]() |
B.圆锥![]() ![]() |
C.直线![]() ![]() ![]() |
D.圆锥![]() ![]() |
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3 . 《九章算术》中关于“刍童”(上、下底面均为矩形的棱台)体积近似计算的注释:将上底面的长乘以二与下底面的长相加,再与上底面的宽相乘,将下底面的长乘以二与上底面的长相加,再与下底面的宽相乘,把这两个数值相加,与高相乘,再取其六分之一,现有“刍童”
,其上、下底面均为正方形,若
,且每条侧棱与底面所成角的正切值均为
,则按《九章算术》的注释,该“刍童”的体积为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9a0c3a4e61b97fa9bc58f3179fc2958.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/343353f850646215dc568fb440fcc0e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
A.8 | B.24 | C.![]() | D.112 |
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名校
4 . 如图,在三棱锥
,
和
均是边长为4的等边三角形,
.
的余弦值并证明:
:
(2)已知平面
满足
,且
平面
,求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6a94d59dee2d5a8f0425b64b2083825.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9f63075fdeeb9e765dd696c4ff43ba1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/147577b4713516176502d95caa0abc74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef5768a8d6630375daf58e971fa200c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99116c812715c5e15ee73d088da4c253.png)
(2)已知平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6754b58cce58c7aac0aa253044d6a388.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/670684ed4962fcebce7b5a140510d066.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0046d5c53d0dbcf95333781bfc86d74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
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5 . 如图,在正方体
中,M,N分别为AC,
的中点,则下列说法中正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
A.![]() ![]() |
B.![]() |
C.直线MN与平面![]() ![]() |
D.异面直线MN与![]() ![]() |
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6 . 如图,在三棱锥
中,
,
是正三角形.
平面
;
(2)若
,
,求
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9128ec5fb5c7b93f19b5951f065c354c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e08b395fcd6ac97b243d81ffa189fac3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78a3fd5284e160896f07ce367645fd04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a8a4d47b010fa15c425bfd7b289b580.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
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2024-06-17更新
|
594次组卷
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2卷引用:福建省福州市部分学校教学联盟2023-2024学年高一下学期期末模拟考试数学试题
7 . 在四棱锥
中,底面ABCD为正方形,
平面ABCD,
,E为线段PB的中点,F为线段BC上的动点,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/829f9180ddd9aa1a0ee0dc520f4e0b5f.png)
A.直线![]() | B.直线AF与平面PBC所成角的最小值是![]() |
C.直线![]() | D.三棱锥![]() |
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8 . 正多面体也称柏拉图立体(被誉为最有规律的立体结构),是所有面都只由一种正多边形构成的多面体(各面都是全等的正多边形).数学家已经证明世界上只存在五种柏拉图立体,即正四面体、正六面体、正八面体、正十二面体、正二十面体.已知一个正八面体
的棱长都是2(如图),则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
A.![]() ![]() |
B.直线![]() ![]() |
C.若点![]() ![]() ![]() ![]() |
D.若点![]() ![]() ![]() ![]() |
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2024-06-11更新
|
991次组卷
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4卷引用:福建省莆田第一中学2023-2024学年高一下学期期中考试数学试题
名校
9 . 如图,在四棱锥
中,
,
,
,E为棱
的中点,
平面
.
平面
;
(2)若二面角
的大小为
,求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34e0a957a55460c72673c0f2ee90dbb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a0e5697eca3f5205cb7b343648240bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/639bec6242a4b3f7bfb4b7033a67328c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f571a1aac46c6d0cf440c0ec2846bf9.png)
(2)若二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1636b4530c0b42d0e0b649e90e3b9e85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30c20e88a33043f4279fff360c81006e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f571a1aac46c6d0cf440c0ec2846bf9.png)
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2024-06-08更新
|
1311次组卷
|
2卷引用:福建省南安市侨光中学2023-2024学年高一下学期第2次阶段考试(5月月考)数学试题
名校
解题方法
10 . 如图,在四棱锥
中,
平面
,
,
,
,
,
,E是
的中点.
平面
;
(2)若直线
与平面
所成的角和
与平面
所成的角相等,求四棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4adf90a8c2b29334cdc5aa5b554991f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f5de5aee06d877b0e0b20517a8fe3f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f8eeeea1c9652cacce976f8129cf520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecf7679c8b4b1e442ce4286d4b0e9c32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97f30533da2e1d2a958dc906c37eba9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e6c2dad46a9052a4185a4f7b4ae8a2e.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e6c2dad46a9052a4185a4f7b4ae8a2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
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