组卷网>知识点选题>等体积法求点面距离
显示答案
| 共计 856 道试题
1 . 在三棱锥中eqIde95134ed803b4ebeaf89e45d5efff006,点eqId2efda802d5534f6d92d9f8af7aaec28beqIdcf2da96900c948a1b3ce7cbfd420c080的中点,eqIdd69c34be5ad0404eb4e0f100980599d3底面eqIda670baf5d73f4d7689915a00c51820f2.
说明: figure
(1)求证:eqId921f847df9f542a999b6cf0a44ab26ac平面eqIdcb27f122349b42bd98ee6c48d59860dc
(2)当eqId0d12bcb7cae84558a7311e912b76c11c时,求点A到平面eqId0902deb68f0b430f932caadd41cd761a的距离;
(3)当k为何值时,eqId2efda802d5534f6d92d9f8af7aaec28b在平面eqId0902deb68f0b430f932caadd41cd761a内的射影恰好为eqId7a004c9db657435db952be9a2365dae5的重心?
2 . 如图,正方体eqId588284d93dc5489295f8f224f8e30d13的棱长为2,E是的棱eqId8f39d706a505485987ccbb3f6177d72d的中点,则点eqIdcfc8599bedfb4ab4944abf141f348a9a到平面eqIdb72e4790644f47429e164f6cc4aaaefb的距离为____
说明: figure
3 . 如图,在多面体eqId9881c5faa5cb449bb37fa59b41c76e43中,eqId907dd22ef7414591bbade3fb5fdade9d均垂直于平面ABCeqIdf85720de909d46f693fa45c2703faa72eqId5e5610ed86b544a4b8b9efea7868350d
说明: figure
(1)求点A到平面eqId5a0fd1dcb23d4219b1483262c39aeb03的距离;
(2)求平面ABC与平面eqId5a0fd1dcb23d4219b1483262c39aeb03所成锐二面角的大小;
(3)求这个多面体eqId9881c5faa5cb449bb37fa59b41c76e43的体积.
4 . 如图所示几何体中,eqIde78cce043a6c43329b55788351ff3484平面eqIda670baf5d73f4d7689915a00c51820f2eqId7af9eac106e04263a9c6d8e4a2a5dcbbeqId18e3ae3e255349039d6726b8293c6cabeqIdbaffac6b458f47bf9fcd80741ce2afe7
说明: figure
(1)当三棱锥eqId12175c05cfe240a0b8270ee03df1962f体积最大时,求三棱锥外接球的表面积.
(2)当eqId63e7bce4e98f4db2a7a08d0e8d88c639时,证明eqId2baa596259a94d0ca637de8281dc781e平面eqIdcb27f122349b42bd98ee6c48d59860dc
(3)当eqId1426e5fc91d94efea17dce85debacef0时,求点eqId052844cae8574a8ab842c38a039baac0到平面eqId0902deb68f0b430f932caadd41cd761a的距离.
5 . 如图,在三棱锥eqId3a31af2cac704f7882626fb78089ea14中,eqId2566f6bfe4174321b87304efe5627fec,平面eqId42ab127176d64d389237593e8dd9c7bf平面eqIda670baf5d73f4d7689915a00c51820f2EF分别是eqId6355576c16ff4047a4bdeff7f7b14185eqIdcf2da96900c948a1b3ce7cbfd420c080的中点.
说明: figure
(1)证明:eqIdd8ee425e980f4d33b46e34f6c7598f61.
(2)若eqId200a003ffdd447cab37975a603b12473eqIdbfafc9c818504a68969d0160bf2b7a65,求C到平面eqId3f2d5304f1fd44b1808666be2c3f28aa的距离.
6 . 如图,在四棱椎eqIdac097205e9cb41279269aadcac3fb6f1中,底面eqId5ce7a06ae7a34393b92b5277978ac014是矩形,eqIde78cce043a6c43329b55788351ff3484底面eqId5ce7a06ae7a34393b92b5277978ac014eqId93cbffaa5ae045d6ac45d1e979991c3aeqIdb53b60c33a254a27b9bfd58e818cc7e6的中点.已知eqIdb60bb1649c8b41cb935771acc097167eeqId12bddb17b1e847129564de449e419f71eqId776c734a36fa4a73a4d27e36f473dace,求:
说明: figure
(1)异面直线eqId0627be51821d4be7b3e024a354815d64eqId7111d4972b7c401c903ff4927c13b5ec所成角的大小;
(2)点eqId8754ce8cf7f34f04abb9a0c041f57f5c到平面eqId83e13ba429bb426fb39bd7720a82c64c的距离.
7 . 如图所示,四棱锥P-ABCD的底面ABCD是边长为1的菱形,∠BCD=60°,ECD的中点,PA⊥底面ABCDPA=2.
说明: figure
(1)证明:平面PBE⊥平面PAB
(2)求点D到平面PBE的距离;
(3)求平面PAD和平面PBE所成锐二面角的余弦值.
8 . 在四棱锥eqIdac097205e9cb41279269aadcac3fb6f1中,eqId3a63d00111554b9e8b896929779a293deqIde43306ee05b74547aa2309375d37775eeqIde78cce043a6c43329b55788351ff3484平面eqId5ce7a06ae7a34393b92b5277978ac014eqId93cbffaa5ae045d6ac45d1e979991c3aeqIdd293923b221045898dcc5442f88aa67a的中点,eqId2381423d4cd146cab95f55527681a766eqId8a76bbe21fb549e3a9c2038d58c7a3d8的中点,eqId86a5fb5508e6440b9ba7ff69feb5dd19
说明: figure
(1)求证∶EM//平面PAC
(2)取PC中点F,证明∶PC⊥平面AEF
(3)求点D到平面ACE的距离.
9 . 已知圆锥的顶点为P,底面圆心为O,半径为1.
说明: figure
(1)设圆锥的母线长为2,求圆锥的表面积和体积;
(2)设eqIda141f69062fe4f00aa825586ed878b6feqId8d993281f7114ae6aedf55eb22e7d4bdeqIdbdb9b3ab33a542d9b1aefcf002989543是底面半径,且eqId79b6b41ec1fa4ce997aea1c11660b503,如图,求直线eqIda668e52822264c18a05bbdd44d38eb84与平面eqIdfcd3aba6b7804fb68706ce7697ffa7a3所成的角的大小.
10 . 已知边长为2的正△eqIda670baf5d73f4d7689915a00c51820f2,现沿高线eqId8a76bbe21fb549e3a9c2038d58c7a3d8翻折而形成四面体eqId5ce7a06ae7a34393b92b5277978ac014,且使得二面角eqId1a8eae54a65b476b90befd98e482f24f的平面角为eqIdf1c3337151994ec4b99354c9d54f311c,则点eqId0cd8063abf2b458f80091bc51b75a904到面eqIda670baf5d73f4d7689915a00c51820f2的距离为_________;此时四面体eqId5ce7a06ae7a34393b92b5277978ac014外接球的表面积为_________.
客服 视频 帮助 公众号 官方微信