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已知某三棱锥的三视图(单位:eqId917ff46970d6499aaa931c004606d813)如图所示,则该三棱锥的外接球的表面积等于________eqId4e590730c1784d8ca08a67a0c4045de4figure
更新:2019/7/18难度系数:0.94题型:填空题组卷:41次
如图,在多面体eqId2588751f06594e188fec5312191ec3a6中,平面eqIde26380849ed449d492cfe2f9e8973edc平面eqId5ce7a06ae7a34393b92b5277978ac014,四边形eqId041ea54dcbeb40308c2dd83660f2cf3b为正方形,四边形eqId5ce7a06ae7a34393b92b5277978ac014为梯形,且eqIdeec1827a5d2841888521a9471977822deqId99ef02e8ce9a4412bb05b19e801c9d1aeqId88f4e1de27bb4951b5ba959a51d379d0
figure
(Ⅰ)求证:eqIdc3e33e534399498cbb3905b3ca4f0ba7平面eqId5e0971e755c24adba699c6b4816dacce
(Ⅱ)求证:eqIdb0f165ed2d8e4524b6c30f463faaf873平面eqId0139652b722b49798a980270e5d2d420
(Ⅲ)在线段eqId1b51efe7c2fa42748ac5a6be262e2fa4上是否存在点eqId2381423d4cd146cab95f55527681a766,使得eqId6928219306984b64b1341b0c5c35c45a平面eqIdb0c10ba23b3a48a2ad1b1618f0a1f37d?若存在,求出eqIdc081d5077efa48b4bfe05b9e19048c52的值;若不存在,请说明理由.
更新:2019/7/18难度系数:0.4题型:解答题组卷:152次
已知eqIde6bc05af65834eadae84eee21da47156是两个不同平面,直线eqIdf0df3c1ffd2d475099c07bbea21e6aea,给出下面三个论断:
eqId6e480eb0dcb34cdfa45374278fc78bb4  ②eqId97b940c602484c649e9ad24e27f68c77  ③eqIdf480d8cc26064a1fabcd202b5b2c9f6c
以其中两个论断作为条件,余下的一个论断作为结论,写出一个正确的命题_______.
更新:2019/7/18难度系数:0.65题型:填空题组卷:42次
某几何体是由一个正方体去掉一个三棱柱所得,其三视图如图所示.如果网格纸上小正方形的边长为1,那么该几何体的体积是___figure
更新:2019/7/18难度系数:0.65题型:填空题组卷:40次
如图,在正方体eqId588284d93dc5489295f8f224f8e30d13中,eqIdd5b10b2a13f148b78e0d5a1b820538fd是棱eqId9773922f56d549e18e0f97d076771cb7上的动点.下列说法正确的是( )
figure
A.对任意动点eqId97e27b61aa384053a5526f74e974dc2f在平面eqIde37223a82dd14db39016756bd377dd6d不存在与平面eqId3a863b4ea75a4f7a9b8015707865c7f3平行的直线
B.对任意动点eqId97e27b61aa384053a5526f74e974dc2f在平面eqId5ce7a06ae7a34393b92b5277978ac014存在与平面eqId3a863b4ea75a4f7a9b8015707865c7f3垂直的直线
C.当点eqIdd5b10b2a13f148b78e0d5a1b820538fdeqId346946f1395a41008d3b3b56c9ae4fbd运动到eqId3f5a5d0fed7d4dc1bcce73cf1b7a92d3的过程中,二面角eqId59a204d0e651425481ae3d1c51059921的大小不变
D.当点eqIdd5b10b2a13f148b78e0d5a1b820538fdeqId346946f1395a41008d3b3b56c9ae4fbd运动到eqId3f5a5d0fed7d4dc1bcce73cf1b7a92d3的过程中,点eqId0cd8063abf2b458f80091bc51b75a904到平面eqId3a863b4ea75a4f7a9b8015707865c7f3的距离逐渐变大
更新:2019/7/18难度系数:0.4题型:单选题组卷:77次
已知eqIdc51cdfd480a54f2db993511e7b1a1508是两条不同的直线,eqIde6bc05af65834eadae84eee21da47156是两个不同的平面,则下列命题正确的是(  )
A.若eqId91ce36f499af47fb827d7d3e37286208,则eqId75becdb8e03a4669b491dd3c7c503418B.若eqId7903625a5cbc4001b5efaec898e2c477,则eqIdbd05ea28c20849798957580086785e2a
C.若eqIddd108086ff4f44e8a13cd0f48ae2fd74,则eqId236517c510e54d7691631b4de8b321d2D.若eqIddb00d145f1504943abfd69f9aa877570,则eqIdbd05ea28c20849798957580086785e2a
更新:2019/7/18难度系数:0.65题型:单选题组卷:128次
在正方体eqId588284d93dc5489295f8f224f8e30d13中,eqIdc3bc315778fd47ef9822f0554c98bd79分别是棱eqIdd38215d368a840cca990386588fdf302的中点,则异面直线eqId1a0830891ff846de8422ea80714ecab4eqId1ebd55a990bc475cb8c343cf06a89e13所成角的大小是(  )
A.eqIdb050c41d1513409598c00ecfe0de8603B.eqIdeacabdda233342049ddc066b54feb1feC.eqId43059a1babed4850ab90728e475e4ce1D.eqId000aef5c9f2a4aa2881d8b6ed91fe140
更新:2019/7/18难度系数:0.65题型:单选题组卷:109次
正三棱柱eqId9881c5faa5cb449bb37fa59b41c76e43(底面是正三角形,侧棱垂直底面)的各条棱长均相等,eqId0cd8063abf2b458f80091bc51b75a904eqIdea82c30b37894b1bb742dee61200db07的中点.eqId2381423d4cd146cab95f55527681a766eqId517584fed25c413ba8b7bb33ffa2d5c6分别是eqIdfe9cbfb067114ce8857e621d77cb5febeqId8f39d706a505485987ccbb3f6177d72d上的动点(含端点),且满足eqIdccf4acf49de7476b83c9541e0a427a92.当eqId1f64331cf3034c38a68946ea0fe1ef14运动时,下列结论中正确的是______ (填上所有正确命题的序号).
figure
①平面eqId49991c7a000a44019e4d9ee4c1c67b66平面eqId50dcbbdb425943e8b5a0e6b8b508d09f
②三棱锥eqId37a09c6f98a24e279f6a1ffa9d5e930a的体积为定值;
eqIdee228a02cb55436fb230451a6e1c2d2a可能为直角三角形;
④平面eqId7cdbd51137094513b26e8e949445b1aa与平面eqId89fbdcb029be4482b52165366491c70f所成的锐二面角范围为eqIdb7eb35e4a7d84d199ab7a0648abf664f
更新:2019/7/17难度系数:0.65题型:填空题组卷:36次
正四面体eqId5ce7a06ae7a34393b92b5277978ac014的棱长为2,棱eqId8b85f650768a40ecb1fff062d3ef52e7平面eqIdc13953f2514e4c8f9c8aaaf5241c33ac,则正四面体上的所有点在平面eqIdc13953f2514e4c8f9c8aaaf5241c33ac内的射影构成的图形面积的最小值是______,最大值是______.
更新:2019/7/17难度系数:0.65题型:填空题组卷:19次
如图,矩形eqId5ce7a06ae7a34393b92b5277978ac014中,eqId72fe3587d8244374a2b6a0904fb8d261eqId42f1c02cc510489799ed224c945a27d2,沿对角线eqId1b51efe7c2fa42748ac5a6be262e2fa4eqIdc1606811a17a43ab89872b189e4eecc5折起,使eqIdcc614bd3390c4d028df189b234dcc351点在平面eqId0f24c9c77eb648e4aade772aaae0eca7内的射影落在eqId0627be51821d4be7b3e024a354815d64边上,若二面角eqIdaf32e72434874d6b843021ebbb8d8081的平面角的大小为eqIdf9db0aee08264a238b9741675591065e,则eqId6f8ec9d4e5f14c8a94dfbd45d5676bc7的值等(  ).
figure
A.eqIddda48cced83d424b89b7d8f8c62b1056B.eqId1df6cfc359dd40dabc2395c51040bf09C.eqId770c1531ed9f4ac6b5e94b48807cf154D.eqIdfa095068b26244c7912a4ce1e7ad060c
更新:2019/7/17难度系数:0.65题型:单选题组卷:44次
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