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1 . 如图,已知四面体
的棱
平面
,且
,其余的棱长均为1.四面体
以
所在的直线为轴旋转
弧度,且始终在水平放置的平面
上方.如果将四面体
在平面
内正投影面积看成关于
的函数,记为
,则函数
的最小值为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/20/b625646d-b6d3-4b96-a5e6-90379cff94f6.png?resizew=211)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/307807ee10071bafbe922eb18d2517d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21ea52361458ce2e49ed0fe99d8e6c02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/782e6aab135b30eed10b49df5a91988d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/782e6aab135b30eed10b49df5a91988d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/20/b625646d-b6d3-4b96-a5e6-90379cff94f6.png?resizew=211)
A.![]() | B.![]() | C.![]() | D.![]() |
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2 . 在棱长为3的正方体
中,点Р是侧面
上的点,且点Р到棱
与到棱AD的距离均为1,用过点Р且与
垂直的平面去截该正方体,则截面在正方体底面ABCD的投影多边形的面积是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ebb05874eb3353d754af24c9974273e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fe734023d4e70010a6b2cc3267cb86e.png)
A.![]() | B.5 | C.![]() | D.8 |
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解题方法
3 . 如图,已知正方体
的棱长为2,M,N分别为
,
的中点.有下列结论:
在平面
上的正投影图为等腰三角形;
②直线
平面
;
③在棱BC上存在一点E,使得平面
平面
;
④若F为棱AB的中点,且三棱锥
的各顶点均在同一求面上,则该球的体积为
.
其中正确结论的个数是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5697ef048e910e7b85ed6bac01056362.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b808a8facf9af30cd8a083010a7b850d.png)
②直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7592c4f01c8e06c7ee90df5b9413a9f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a40d8806b86572352ed08aa2b7f89f7.png)
③在棱BC上存在一点E,使得平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcadc521b53fabecc10ed30fe8d96c2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ee5a94f9063a71581f409e47ebaf602.png)
④若F为棱AB的中点,且三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48b5d7a90614288e46bebdb611e9bd23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eefdcd39676298f214654051fc51ba92.png)
其中正确结论的个数是( )
A.0 | B.1 | C.2 | D.3 |
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2022-07-12更新
|
3249次组卷
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12卷引用:四川省成都市2023届高三上学期摸底考试文科数学试题
四川省成都市2023届高三上学期摸底考试文科数学试题四川省成都市2023届高三摸底测试理科数学试题安徽省宣城中学2023届高三原创模拟金卷(一)数学试题第一章 空间向量与立体几何单元测试(巅峰版)(已下线)第04讲 空间直线、平面的垂直 (讲)-1(已下线)考向25空间几何体的结构、三视图和直观图(重点)山西省运城市景胜中学2022-2023学年高二上学期9月月考数学(A)试题(已下线)考向26空间几何体的表面积与体积(重点)-2河南省南阳市第八中学校2022-2023学年高二上学期第一次线上考试(月考)数学试题广东省珠海市斗门区第一中学2022-2023学年高二上学期期中数学试题天津市新四区示范校2022-2023学年高一下学期期末联考数学试题河南省周口市周口恒大中学2023-2024学年高二下学期5月月考数学试题
名校
4 . 如图,等腰三角形ABC在平面α上方,∠BAC = 90°,若△ABC以BC为旋转轴旋转,形成的旋转体在平面α内的投影不可能的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/3/c8806296-3d71-4243-b773-f9dec4a20f52.png?resizew=159)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/3/c8806296-3d71-4243-b773-f9dec4a20f52.png?resizew=159)
A.![]() | B.![]() | C.![]() | D.![]() |
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5 . 在空间直角坐标系
中,已知
,
,
,
,若
,
,
分别表示三棱锥
在
,
,
坐标平面上的正投影图形的面积,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a834024400d0730af3e640ca4d5f54b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b889a93a6b77ffd108de41bc470d08f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97ecf78090de9b894a74602892e5412b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd471a3e64b76d4c5944458aeb707297.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77e8611b09c15dfea54a36bf8a15cd29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6899bf9cadae2ccdb14cbc87d4f280ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4357d5744046d4d44abb09e1ee35fcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ef1e8a88d934eca5399decc64fdbd43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddd48d1ef9e8cd3b7aea60fd95b70fb6.png)
A.![]() | B.![]() ![]() |
C.![]() ![]() | D.![]() ![]() |
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2021-09-08更新
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205次组卷
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3卷引用:青海省西宁市城西区青海湟川中学2020-2021学年高二上学期期中数学试题
名校
6 . 如图,直线
平面
,垂足为
,正四面体
的棱长为2,
,
分别是直线
和平面
上的动点,且
,则下列判断:①点
到棱
中点
的距离的最大值为
;②正四面体
在平面
上的射影面积的最大值为
.其中正确的说法是.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/22/ad8a8194-89ed-4d80-800d-bd6ac7a87a8f.png?resizew=232)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9df740160690029ac1e730c85f20347.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](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/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa145a3e4f18f784ddf4869e0bf904c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1f190b17530d81d927c358ac84757a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/22/ad8a8194-89ed-4d80-800d-bd6ac7a87a8f.png?resizew=232)
A.①②都正确 | B.①②都错误 | C.①正确,②错误 | D.①错误,②正确 |
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2020-05-21更新
|
486次组卷
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2卷引用:2020届上海市黄浦区高三二模(阶段性调研)数学试题
7 . 如图直线
平面
,垂足为
,正四面体
的棱长为2,
在平面
内,
是直线
上的动点,则当
到
的距离为最大时,正四面体在平面
上的射影面积为
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/23/a6cadbad-99e9-49c2-a6db-7905ff607315.png?resizew=173)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9df740160690029ac1e730c85f20347.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/23/a6cadbad-99e9-49c2-a6db-7905ff607315.png?resizew=173)
A.![]() | B.![]() | C.![]() | D.4 |
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8 . 如图,四面体ABCD各棱长均相等,E,F分别是AC,AD的中点,则
在平面ABD上的射影是.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/7/b5bf4e9f-82bc-46d4-bc7d-b6756b73b849.png?resizew=140)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f2ea13010e2399194be2a681310543e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/7/b5bf4e9f-82bc-46d4-bc7d-b6756b73b849.png?resizew=140)
A.![]() | B.![]() | C.![]() | D.![]() |
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9 . 如图所示,在正方体ABCD﹣A1B1C1D1中,M为DD1的中点,则图中阴影部分BC1M在平面BCC1B1上的正投影是( )
![](https://img.xkw.com/dksih/QBM/2019/1/14/2118614208421888/2118759998095360/STEM/188471ad-df3b-4bee-a10f-5a219b08405f.png?resizew=210)
![](https://img.xkw.com/dksih/QBM/2019/1/14/2118614208421888/2118759998095360/STEM/188471ad-df3b-4bee-a10f-5a219b08405f.png?resizew=210)
A.![]() | B.![]() | C.![]() | D.![]() |
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2019-01-14更新
|
420次组卷
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8卷引用:【市级联考】广东省珠海市2019届高三9月摸底考试数学(文)试题
【市级联考】广东省珠海市2019届高三9月摸底考试数学(文)试题【全国百强校】黑龙江省哈尔滨六中2018-2019学年高二(上)期中考试数学(文)试题【全国百强校】江西省南昌市第十中学2019届高三上学期期中考试数学(理)试题【市级联考】河北省张家口市2019届高三上学期期中考试数学文试题(已下线)专题8.1 空间几何体的结构、三视图和直观图(练)-浙江版《2020年高考一轮复习讲练测》(已下线)专题8.1 空间几何体及其三视图和直观图(精讲)-2021年新高考数学一轮复习学与练(已下线)专题8.1 空间几何体及其三视图和直观图(精练)-2021年新高考数学一轮复习学与练(已下线)专题8.1 空间几何体及其三视图和直观图(练)-2021年新高考数学一轮复习讲练测
10 . 如图,在正方体
中,
分别是
,
的中点,则四面体
在平面
上的正投影是
![](https://img.xkw.com/dksih/QBM/2018/7/3/1980696592719872/1982214190292992/STEM/c035d867bf6a41db942b8316142c9f64.png?resizew=117)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb49fdc6b6bbb2449fdf8a0de769d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42c2d86d8daea5e652d99fe1c6bc3f9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c95c0160e73beb94a4a1cbc0168e9a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f86dd74047dacc6c23e24bff4c40d947.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/611f100dcfa7803db6eb233e2e7f2dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c52091eb745de866044477641a7c55f.png)
![](https://img.xkw.com/dksih/QBM/2018/7/3/1980696592719872/1982214190292992/STEM/c035d867bf6a41db942b8316142c9f64.png?resizew=117)
A.![]() | B.![]() | C.![]() | D.![]() |
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