伤城文章网 >  > 最新-2018届高三数学第一轮复习单元测试(8)—《立体几何》 精品

最新-2018届高三数学第一轮复习单元测试(8)—《立体几何》 精品


2018 届高三数学第一轮复习单元测试(8)—《立体几何》 一、 选择题(本大题共 12 小题,每小题 5 分,共 60 分.在每小题给出的四个选项中,只有一项是符合题 目要求的) 1. (2018 浙江文卷)对两条不相交的空间直线 a 与 b,必存在平面α ,使得 ( ) (A) a ? ? , b ? ? (B) a ? ? , b ∥α (C) a ? ? , b ? ? (D) a ? ? , b ? ? 2.将正方形 ABCD 沿对角线 BD 折成一个 120°的二面角,点 C 到达点 C1,这时异面直线 AD 与 BC1 所成角的余弦值是 ( ) A. 2 2 B. 1 2 C. 3 4 D. 3 4 ) 3.一个长方体共一顶点的三个面的面积分别是 2 、 3 、 6 ,这个长方体对角线的长为( A.2 3 B.3 2 C.6 D. 6 0 4.已知二面角α -l-β 的大小为 60 ,m、n 为异面直线,且 m⊥α ,n⊥β ,则 m、n 所成的角为 ( ) A.30 B.60 C.90 5.如图,在正三角形 ABC 中,D、E、F 分别为各边的中点, G、H、I、J 分别为 AF、AD、BE、DE 的中点.将△ABC 沿 DE、EF、DF 折成三棱锥以后,GH 与 IJ 所成角的度 数为 ( ) A.90° B.60° C.45° D.0° 6.两相同的正四棱锥组成如图所示的几何体,可放棱长 为 1 的正方体内,使正四棱锥的底面 ABCD 与正方 体的某一个平面平行,且各顶点 均在正方体的面上, ... 则这样的几何体体积的可能值有 A.1 个 C.3 个 B.2 个 D.无穷多个 0 0 0 D.120 0 A H G F C J D I ( B) E 2 7. (2018 山东文卷)右图是一个几何体的三视图,根据图中数据, 3 可得该几何体的表面积是 ( ) A. 9 π B. 10π 2 2 C. 11π D. 12π 俯视图 正(主)视图 侧(左)视图 8. (理)高为 5,底面边长为 4 3 的正三棱柱形容器(下有底) ,可放置最大球的半径是( A. ) 3 2 D. 2 2 (文)三个两两垂直的平面,它们的三条交线交于一点 O,点 P 到三个平面的距离比为 1∶ 3 2 B.2 C. 2∶3,PO=2 14 ,则 P 到这三个平面的距离分别是 A.1,2,3 B.2,4,6 C.1,4,6 D.3,6,9 ( ) 9.如图,在四面体 ABCD 中,截面 AEF 经过四 面体的内切球 (与四个面都相切的球) 球心 O, 且与 BC,DC 分别截于 E、F,如果截面将四 面体分成体积相等的两部分,设四棱锥 A- BEFD 与三棱锥 A-EFC 的表面积分别是 S1, S2,则必有 ( ) A.S1?S2 B.S1?S2 C.S1=S2 D.S1,S2 的大小关系不能确定 A O D F B E C 10. 已知球 o 的半径是 1,ABC 三点都在球面上,AB 两点和 AC 两点的球面距离都是 面距离是 A. p 4 p ,BC 两点的球 4 p ,则二面角 B-OA-C 的大小是 3 ( p 2 ) B. p 3 C. D. 2p 3 11.条件甲:四棱锥的所有侧面都是全等三角形,条件乙:这个四棱锥是正四棱锥,则条件甲是 条件乙的 ( ) A.充分不必要条件 B.必要不充分条件 C.充要条件 D.既不充分也不必要条件 12.已知棱锥的顶点为 P,P 在底面上的射影为 O,PO=a,现用平行于底面的平面去截这个棱 锥,截面交 PO 于点 M,并使截得的两部分侧面积相等,设 OM=b,则 a 与 b 的关系是 ( ) A.b=( 2 -1)a C.b= B.b=( 2 +1)a 2 ? 2a 2 ? 2a D.b= 2 2 二、填空题(本大题共 4 小题,每小题 4 分,共 16 分.把答案填在题中的横线上) 13 .已知正四棱锥的体积为 12 ,底面对角线的长为 2 6 ,则侧面与底面所成的二面角等于 _______________. 14.若一条直线与一个正四棱柱各个面所成的角都为 ? ,则 cos ? =______. 15.若棱长为 3 的正方体的顶点都在同一球面上,则该球的表面积为___________. 16.多面体上,位于同一条棱两端的顶点称为相邻的, C1 如图,正方体的一个顶点 A 在平面 ? 内,其余顶 D1 点在 ? 的同侧,正方体上与顶点 A 相邻的三个顶 A1 点到 ? 的距离分别为 1,2 和 4,P 是正方体的其 C 余四个顶点中的一个,则 P 到平面 ? 的距离可能 D 是: ( ) B ①3; ②4; ③5; ④6; ⑤7 ? A 以上结论正确的为______________. (写出所有正 A1 第 16 题图 确结论的编号 ) .. B1 三、解答题(本大题共 6 小题, 共 74 分,解答应写出文字说明,证明过程或演算步骤) 17. (本小题满分 12 分)在长方体 ABCD ? A1 B1C1 D1 中,已知 DA ? DC ? 4, DD1 ? 3 ,求异面 直线 A1 B 与 B1C 所成角的大小(结果用反三角函数值表示). 18. (本小题满分 12 分)如图, l1 、 l2 是互相垂直的异面直线,MN 是它们的公垂线段。点 A、B 在 l1 上,C 在 l2 上, AM ? MB ? MN . (1)证明 AB ⊥ NB ; (2)若 ?ACB ? 60 ,求 NB 与平面 ABC 所成角的余弦值. O 19. (本小题满分 12 分)如图,在棱长为 1 的正方体 ABCD ? A1 B1C1 D1 中, p 是侧棱 CC1 上 的一点, CP ? m . (1)试确定 m ,使得直线 AP 与平面 BDD1 B1 所成角

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