1 . 如图,正方体
中,
,点
分别是棱
的中点.
的结构特征,判断该几何体是哪种多面体,并结合该类多面体的定义给出证明;
(2)求多面体
的表面积和体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/334bd1a151c0a42ca813cb6b839ce45c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe1b448a14b6c26040126e4d67fcb9c5.png)
(2)求多面体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe1b448a14b6c26040126e4d67fcb9c5.png)
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2 . 已知正三棱台
中,
,
,
、
分别为
、
的中点.
(1)求该正三棱台的表面积;
(2)求证:
平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad1a56baf43ffdf67bc8460856e31fec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5825e3891ce507d4af2e0d9d1a0b74b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/24/816f0559-5515-4880-98dc-f2a85b6ee195.png?resizew=160)
(1)求该正三棱台的表面积;
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8d2d217e9bcd059908f117dfc4d4259.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
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3 . 如图,在三棱台
中,AB=BC=CA=2DF=2,FC=1,∠ACF=∠BCF=90°,G为线段AC中点,H为线段BC上的点,
平面FGH.
(1)求证:点H为线段BC的中点;
(2)求三棱台
的表面积;
(3)求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8783bc74553bf44b61d999a0e4144bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e3c0430146b7b8d40ebb721a4d0de19.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/16/b0fae38b-b027-4666-9f69-43d3c14ecac9.png?resizew=153)
(1)求证:点H为线段BC的中点;
(2)求三棱台
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8783bc74553bf44b61d999a0e4144bb.png)
(3)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/885f72d31be9531c291862733e4f01c0.png)
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4 . 如图,在三棱台
中,
,
,
,
为线段
中点,
为线段
上的点,
平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/6/127b444e-6732-41c5-9a20-7be38b98a4f7.png?resizew=192)
(1)求证:点
为线段
的中点;
(2)求三棱台
的表面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8783bc74553bf44b61d999a0e4144bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a42a3bc9ecc4fe62d1f4dabdda44cc8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a7ee687c3ad4a6e97315491c619fc94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff95fcab3b2f6dfd6c6098f2272567b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/debdc6632a4877e5131d3da25cda8b89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1828e73ec5e00f95aa11ff74c703a5c1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/6/127b444e-6732-41c5-9a20-7be38b98a4f7.png?resizew=192)
(1)求证:点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
(2)求三棱台
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8783bc74553bf44b61d999a0e4144bb.png)
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5 . 已知底面边长和斜高长均为2的正四棱锥被平行于底面的平面所截得的正棱台为
,且满足
.
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea9dcbb4a05aa3b0cf780baa4489556e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b54387f870ae37f7951b253665d64f6.png)
(2)求棱台的体积
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be54e84508decfcce6d2fcbe6c8c1a92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
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6 . 如图,圆台
的轴截面为等腰梯形
,
,
,
,圆台
的侧面积为
.若点C,D分别为圆
,
上的动点且点C,D在平面
的同侧.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/4/38910484-ae81-496f-96ff-0784986be22b.png?resizew=207)
(1)求证:
;
(2)若
,则当三棱锥
的体积取最大值时,求多面体
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e65ac334119ccd6204402a7aba29a55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10fee8f3cec7f73237eeb6119505b624.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a23ebc15ea66abe2eb975cf527b368dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5fdcd878ae4edaff14f1647ecc36e7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/570f8b295ee0c7c60e6fe1dbf054ff52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e65ac334119ccd6204402a7aba29a55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/997b5842f3d4eae1989debee9ae41b9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c4f6f74444b2b7947fc6e35c8d62322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10fee8f3cec7f73237eeb6119505b624.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/4/38910484-ae81-496f-96ff-0784986be22b.png?resizew=207)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/143bc52bf615596ee5d707e8c9592018.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a889f4f060164fb2fc57471b93183633.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31c380651bb919db7111650d73a46c01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e10df339e7f7055c5699236359ceaea.png)
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2020-04-08更新
|
1327次组卷
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3卷引用:云南师范大学附属中学2019-2020学年高三适应性月考(六)数学(文)试题
云南师范大学附属中学2019-2020学年高三适应性月考(六)数学(文)试题四川省泸州市泸县第二中学2020届高三下学期第四次学月考试数学(文)试题(已下线)考点24 空间几何体体积及表面积(练习)-2021年高考数学复习一轮复习笔记