如图,在正方体
中,E是
的中点.
平面ACE;
(2)若
,求三棱锥B—AEC的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0424446817f60c18f8e4e3cc202ad99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb96d9ea39bf7974143973559058dbec.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0387c9dd6759a28c8beceef04f8a5a62.png)
更新时间:2024-05-25 01:45:30
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相似题推荐
解答题-问答题
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较易
(0.85)
名校
解题方法
【推荐1】已知在四棱锥
中,
,
,
,
,
且平面
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/4/55d5d046-5c3d-4a26-bac4-851c060b8c51.png?resizew=165)
(1)设点
为线段
的中点,试证明
平面
;
(2)若直线
与平面
所成的角为60°,求四棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b1e038b4e76b3a368731d3331522b8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0137c721b8d4ea6dca8b7d9761134726.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/615fc8790237a1b09af51d6bcad6b595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0028211551dd418eaaf51dde450f8b73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5545dc3211671941048034af38092fa6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/236c134aad7d9a21c49c07e924b9a531.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de8ff58f671a287701011a1b31e67e28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/4/55d5d046-5c3d-4a26-bac4-851c060b8c51.png?resizew=165)
(1)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a5f445af1ae136773cb338920552ff2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5a77c5da4ad115082a32aa38817f5cd.png)
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【推荐2】如图所示,四棱锥
中,
(
是四棱锥
的高),![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0391c245d702d875f90ec233a69adcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e735a28578ba191da6d4f3b0f8e8729.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d2eea6bad81c91d7bf6555545181109.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccfd3cc8d727f5d4f41c834f6851a094.png)
为线段
上一点,
,
为
的中点.
![](https://img.xkw.com/dksih/QBM/2018/4/19/1927333674254336/1930288469016576/STEM/88f3ac441a2c4c5193ed7cb2eb7155cd.png?resizew=215)
(1)证明:
平面
;
(2)求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b888abe74a0038fefb5e1ff92c78b736.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0391c245d702d875f90ec233a69adcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e735a28578ba191da6d4f3b0f8e8729.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d2eea6bad81c91d7bf6555545181109.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccfd3cc8d727f5d4f41c834f6851a094.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bd940068856d423dd049fb345881736.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eeef1db30212433062b3297569a7aafd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://img.xkw.com/dksih/QBM/2018/4/19/1927333674254336/1930288469016576/STEM/88f3ac441a2c4c5193ed7cb2eb7155cd.png?resizew=215)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7592c4f01c8e06c7ee90df5b9413a9f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1318239c0348e0ba82490206bff3a91e.png)
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解题方法
【推荐1】如图,在多面体
中,四边形
是正方形,
平面
,
平面
,
.
的中点,求证:
平面
;
(2)若多面体
的体积为32.求m的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f4c3f9dd5d0343597a7f58a1989b537.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac0b72906641ed13716cfbce50923282.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/951cfccd19a911408f8671f9b7dd1b4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a48f3a086c6961c5ba7e121a4e60738e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/134ef0b1a2669a09f05bd4dc2496f706.png)
(2)若多面体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
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【推荐2】小明同学参加综合实践活动,设计了一个封闭的包装盒,包装盒如图所示:底面
是边长为
(单位:
)的正方形,
、
、
、
均为正三角形,且它们所在的平面都与平面
垂直.证明:
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3304e23f3b0f9569c4140ca89b6498.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9efa9fbcfb9595e2f031aa691db4564b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f14b86b8bf99386fc939c9c12b1355ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6a0c85deb80d8e63bc60127e803f7ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7ab8de2231d3bfbd289dcdf6d512667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6801e866d3f9f26886e271708a73a6b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f9d682e5d3cc8573574d8d11636758.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/7/7f967582-5d05-4bd1-96c4-eeeb9e4a7f81.png?resizew=220)
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