名校
1 . 已知三棱锥
的四个顶点在球O的球面上,
,
是边长为6的正三角形,E为SA的中点,直线CE,SB所成角为90°,则球O的表面积为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41e5db1d2fd912f77923e4c120a7dc19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/700f2f0f1cf306f7fc18d18fe91d0acb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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解题方法
2 . 如图1,在等腰梯形ABCD中,
,
,E为CD中点,将
沿AE折起,使D点到达P的位置(点P不在平面ABCE内),连接PB,PC(如图2),则在翻折过程中,下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a11029ca6b4b9e7f777af0280cf163c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edba78154f762c0b636754c88cf90b5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63b43490ca09467a4c8cd8cfe91c94e4.png)
A.![]() | B.![]() |
C.存在某个位置,使![]() | D.PB与平面ABCE所成角的取值范围为![]() |
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解题方法
3 . 已知正方体
的棱长为2,点
为平面
内一动点,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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
A.若点![]() ![]() ![]() ![]() |
B.若点![]() ![]() ![]() ![]() |
C.若点![]() ![]() ![]() |
D.若点![]() ![]() ![]() ![]() ![]() |
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解题方法
4 . 如图,在四棱锥P-ABCD中,底面ABCD为平行四边形,
,
,
,
,
,点N在棱PC上,平面
平面
.
;
(2)若
平面
,求三棱锥
的体积;
(3)若二面角
的平面角为
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e918b70b02a73685e3c536c7f380e2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3ad66112b09c909cab417085702ec00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37002ada5d194d4d062fa3285d7d9824.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b235d0737ddc0d2c85abd4484c10d76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f04c222223dae9ef27d4c132534d9848.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9e5f1cfea3643c30c21732073a11ef.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/373f735f0f04d11f1951eaef1bb78b6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfaf581b4f42a25087f7eee23a7d66b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5a94e7ab62cf6374d2e4c6d7240a271.png)
(3)若二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/957c57e018a7086ff1c1f823e02b7ef7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15615de1a6df206dbd081251f676578e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50cafe199913787a939fe9e100924023.png)
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5 . 如图,在四棱锥
中,
平面
,
,
,
,
.
平面
.
(2)若
为线段
的中点,求平面
与平面
的夹角的余弦值.
![](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/9060f03b9ee41d70d135b1e1a8902ce9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c3ca1c27bdc0102bf2c6b306ddd1d95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f121eabff3c62c1a196d9ca5f6f83f0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97f30533da2e1d2a958dc906c37eba9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e40cae1138ce408cf7ebbe14f152d6e9.png)
您最近一年使用:0次
2024-06-08更新
|
411次组卷
|
2卷引用:浙江省培优联盟2023-2024学年高二下学期5月联考数学试题
名校
解题方法
6 . 矩形ABCD中,
,将
沿BD向上对折至
位置.
在平面BCD上的射影落在BC上,求证:
;
(2)在对折过程中,求平面
与平面BCD所成角的正切的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d5d826b6d826ba34193f6f65964dd77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3ea25ef38e4afa8f75ffd0842890289.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac7856b843caf384fca612ce663f21c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/646e85f3bca49449292f7ee9cc650a6f.png)
(2)在对折过程中,求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1530d93834fbafba5f7217778ea90442.png)
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7 . 如图,在三棱锥
中,已知
.
;
(2)求侧面
与侧面
所成的二面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41e5db1d2fd912f77923e4c120a7dc19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c90d7e37f2fe4b59fa38e39f816c44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22b04a4591698f4f2a472f7ed6088674.png)
(2)求侧面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21665d21bbfb04410c78345de1fd15ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc9c9cfa597b444b5c9dbae7a825a695.png)
您最近一年使用:0次
2024-05-27更新
|
484次组卷
|
2卷引用:浙江省强基联盟2023-2024学年高一下学期5月期中考试数学试题
名校
解题方法
8 . “风筝”是中国传统文化中不可或缺的一部分,距今已有2000多年的历史.相传在东周春秋时期,墨翟以木头制成木鸟,是人类最早的风筝起源.后来鲁班用竹子,改进墨翟的风筝材质,直至东汉期间,蔡伦改进造纸术后,坊间才开始以纸做风筝,称为“纸鸢”.到南北朝时,风筝开始成为传递信息的工具;从隋唐开始,由于造纸业的发达,民间开始用纸来裱糊风筝;到了宋代的时候,放风筝成为人们喜爱的户外活动.风筝主要由骨架、风筝面、尾翼、提线、放飞线五部分组成.如图(1)就是一个由菱形的风筝面ABCD和两个直角三角形尾翼
和
所组成的风筝.其中
,
,
,
,
.现将此风筝的两个尾翼分别沿
折起,使得点P与点Q重合于点S,并连结
,得到如图(2)所示的四棱锥
.
平面
;
(2)若E为棱
上一点,记![](https://staticzujuan.xkw.com/quesimg/Upload/formula/968088978992ba767468dec2dc436350.png)
①若
求直线
与平面
所成角的正切值;
②是否存在点E使得直线
与直线
所成角为
,若存在请求出
的值,若不存在请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d41984f53bb280ba8b5ac00a52ce2825.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d96645a3530e72d5d733d2c72147d340.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb8fb552b9e21dbaba74d11aa747790.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37002ada5d194d4d062fa3285d7d9824.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d899b31ac8800258c52e86a70e7ab9ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4aca5534bce25acaeb7379deed8f8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a0f2f623bbe6beb1fdbc767bc1ba70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a887678ca42faa3d289e2b6460790b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b5e290c6b2c5508a3bf6117afbf7e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e56fdf217165748fafe938b64fa08179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5000fea066102e62cf2128ccbbd2b3e3.png)
(2)若E为棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a6e2867f32d3f1c3cd36cd3a11a8580.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/968088978992ba767468dec2dc436350.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1c3ea872a20fdc1843cb5ffce8a554.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5000fea066102e62cf2128ccbbd2b3e3.png)
②是否存在点E使得直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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解题方法
9 . 在棱长为的正方体
中,
为底面
的中心,
为线段
的中点,则
( )
A.![]() ![]() |
B.三棱锥![]() ![]() |
C.存在两个不同的![]() ![]() |
D.![]() ![]() ![]() |
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10 . 平行四边形
中,
,点
为
的中点,将
沿
折起到
位置时,
.
;
(2)求平面
与平面
的夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc050ef97ba7177c8270cbd6a018c9c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b37793a3a810e823e10c340986f55ddd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6eea78bf026d76f1cb9cc3dc9349a193.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cc72a44dad13532cb9ddcc64bd78105.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b37793a3a810e823e10c340986f55ddd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/218054144a13435580cd132b9459546c.png)
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