组卷网>高中数学综合库>空间向量与立体几何>空间几何体>空间几何体的表面积与体积>柱、锥、台的体积>锥体体积的有关计算
题型:多选题 难度:0.4 引用次数:414 更新时间:2021/5/7 15:56:43 题号:12867883
在棱长为1的正方体eqId588284d93dc5489295f8f224f8e30d13中,eqId80024c560b2a4efc8e3275bcf0f79ebb分别为eqIdfe9cbfb067114ce8857e621d77cb5febeqIde4682078ddd9488281e376503edb4f95的中点,则下列结论中正确的是(   )
A.平面eqId81dac8f6b9e94a8c814fe471937c55e6平面eqId510a0efa86b64e78aaf9828262eb06aaB.直线eqId3be2cc74b5df4257b116d1672859cb5e与平面eqId1ea7f8da25d94506ac4bc2f62f837ac9所成角为eqId4023ceb292e24a45871ca56fa44d50e3
C.直线eqId3dd88fd134c1472886302db0246dfc44与直线eqIdcf2da96900c948a1b3ce7cbfd420c080所成角为eqIdd01b7918993a412cb774dea127f210b6D.四棱锥eqIdb29d103037c04b8184ef23fb3c7698d0的体积为eqId9e311be638c64d4eaed28e15dcba7451

类题推荐

【推荐1】如图,直三棱柱eqId9881c5faa5cb449bb37fa59b41c76e43中,所有棱长均为1,点eqId93cbffaa5ae045d6ac45d1e979991c3a为棱eqIdbd70ef61616a454bae30f5691884094b上任意一点,则下列结论正确的是(   )
说明: figure
A.直线eqIdea82c30b37894b1bb742dee61200db07与直线eqId1dcb20a9ce8d4076af5dd64f7066c6d6所成角的范围是eqIdf1a598d767874f3b8c7076f0c0e731eb
B.在棱eqIdbd70ef61616a454bae30f5691884094b上存在一点eqId93cbffaa5ae045d6ac45d1e979991c3a,使eqId92c3f8299e50439b8442b2c3bf55669f平面eqId8b0874e3e1f2410e981eb17d1079bb05
C.若eqId93cbffaa5ae045d6ac45d1e979991c3a为棱eqIdbd70ef61616a454bae30f5691884094b的中点,则平面eqId9f4208fa07f24bc69ce1bf42c811eec2截三棱柱eqId9881c5faa5cb449bb37fa59b41c76e43所得截面面积为eqIdb0d1f3cbae234989a8a1f684c2de58fd
D.若eqId63db14a5b4334f3ea583c8fb12b0d175为棱eqId31581e8b21734ef88d2a14232de7e7a6上的动点,则三棱锥eqIdce4949a7ca7e4213a5589ad1c87b1257体积的最大值为eqId0dce1f07f2a0460f80cd56ad0d9328c2
更新:2021/04/15组卷:928
多选题 | 较难(0.4) |
【推荐2】已知边长为2的等边eqId64b9b599fdb6481e9f8d9a94c102300b,点eqId0cd8063abf2b458f80091bc51b75a904eqId93cbffaa5ae045d6ac45d1e979991c3a分别是边eqIdcf2da96900c948a1b3ce7cbfd420c080eqId99a3187c2b8f4bcc9703c74c3b72f1f3上的点,满足eqId1bafa99adc0841e5b1776bc66f3c2637eqId53d1a8ec4f6d4c48a0ec21dd4bcd8063eqId8fd22528d34a4903a261e1511957c286),将eqId1ba8a6a849e04b31abd4a64a759061b5沿直线eqId66d409c343f04cfda647f9bfc7da6b2a折到eqId7a2152e413ad4fd7b8b801ffd11ff9fc的位置,在翻折过程中,下列结论成立的是(   )
说明: figure
A.在边eqIda70897d1894e4abf8f1e1ed3929ac655上存在点eqId63db14a5b4334f3ea583c8fb12b0d175,使得在翻折过程中,满足eqId3f99c0ec5dbb4b91a354d259cf074b97平面eqId9259b58682c149d6b23e4008d9b52bf8
B.存在eqId6d9952ee0da149268ec810020557cb1a,使得在翻折过程中的某个位置,满足平面eqIdadc43aea83574782b6bfdf7cbeeff6cd平面eqIdda27baf162634ddaab4c30f70ed6eb60
C.若eqIdd9692b11f94548e0a1f8a8b2b22dfce2,当二面角eqIdeb90f768e22544d1adf2330f2a2728ad等于60°时,eqIdfb9307c4b0984fb19c56117a77cd80b2
D.在翻折过程中,四棱锥eqIdab40a927743a4939a59ee6939e493635体积的最大值记为eqId7594e055d8fc45908633b040f444d5ddeqId7594e055d8fc45908633b040f444d5dd的最大值为eqIdc32dbe4815624f89bddb46c830653a04
更新:2020/10/22组卷:991
多选题 | 较难(0.4) |
【推荐3】如图四棱锥eqIdac097205e9cb41279269aadcac3fb6f1,平面eqId3084aa1e379e4f168e9c2332df2ca9df平面eqId5ce7a06ae7a34393b92b5277978ac014,侧面eqIde5632d7e0a9540bfa77df0f3f1091dc8是边长为eqIdcb0b4d348f474513aaf4718b21559f01的正三角形,底面eqId5ce7a06ae7a34393b92b5277978ac014为矩形,eqId49b3c2d3845444bb847b06bf9f5f8116,点eqId75a143b898e14ccdb032561fba9da811eqIdd293923b221045898dcc5442f88aa67a的中点,则下列结论正确的是(   )
说明: figure
A.eqId46066cc81fd545c3b9f7c65d8d19beec平面eqIde5632d7e0a9540bfa77df0f3f1091dc8
B.eqIdb53b60c33a254a27b9bfd58e818cc7e6与平面eqIdd50900e06877472f9e2c5090434a6392所成角的余弦值为eqIdd1ebfa5c81a04d18900d19595d070677
C.三棱锥eqId946fc5850ab84034a0ed57146a965f5d的体积为eqIdf35f1e45d1d840c2ae8371573f781126
D.四棱锥eqId7c13d9f034334a9dabd01fc8a98ee404外接球的内接正四面体的表面积为eqIddbf88414577842e198b1155a1446143e
更新:2020/07/21组卷:1507
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