1 . 如图,在直三棱柱
中,
,
.
(1)设平面
与平面
的交线为l,判断l与
的位置关系,并证明;
(2)若
与平面
所成的角为
,求三棱锥
内切球的表面积S.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9af89996db5c5b01c09a448c8e2e47b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1240a927e5540d2dce76ba019f6cf82.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/7/3650d5da-c50e-4f71-b5f2-8d80f60bd852.png?resizew=162)
(1)设平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9539f8fb13345b449274b67bbda995db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6b86c22b670a8e9f3896f9e8883fbbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d38593653bedb845ecfa820806a29a1e.png)
您最近一年使用:0次
名校
解题方法
2 . 如图1,菱形ABCD中∠ABC=120°,动点E,F在边AD,AB上(不含端点),且存在实数
使
,沿EF将△AEF向上折起得到△PEF,使得平面PEF⊥平面BCDEF,如图2所示.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/28/fc808256-a8c2-4605-94da-7d42da3a24a5.png?resizew=364)
(1)若BF⊥PD,设三棱锥P-BCD和四棱锥P-BDEF的体积分别为
,
,求
;
(2)当点E的位置变化时,平面EPF与平面BPF的夹角(锐角)的余弦值是否为定值,若是,求出该余弦值,若不是,说明理由;
(3)若AB=2,求四棱锥P-BDEF的外接球半径的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ceeb60f40e8d5b6fc184be29ce3d4bd0.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/28/fc808256-a8c2-4605-94da-7d42da3a24a5.png?resizew=364)
(1)若BF⊥PD,设三棱锥P-BCD和四棱锥P-BDEF的体积分别为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4764374bd2fb78e59cd0b283637baeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63055a5d6916f99d07fede49120753f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f737b04ce09bc7e1ed86dc9b3c85203b.png)
(2)当点E的位置变化时,平面EPF与平面BPF的夹角(锐角)的余弦值是否为定值,若是,求出该余弦值,若不是,说明理由;
(3)若AB=2,求四棱锥P-BDEF的外接球半径的最小值.
您最近一年使用:0次
3 . 如图,AB是圆柱
的一条母线,BC过底面圆心O,D是圆O上一点.已知
,
(2)将四面体ABCD绕母线AB所在的直线旋转一周,求
的三边在旋转过程中所围成的几何体的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/270ddac9587bf1ea553914cb69595ab2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50be1057156b40a5f6b87be5194d728.png)
(2)将四面体ABCD绕母线AB所在的直线旋转一周,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac451db3443cabb204f96c31fd4a02e.png)
您最近一年使用:0次
2022-07-08更新
|
901次组卷
|
7卷引用:重庆市巫山大昌中学校2021-2022学年高一下学期期末数学试题
解题方法
4 . 如图,在四棱锥
中,底面
是边长为
的菱形,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e075468e7fb0bf30229aec01a7205977.png)
为正三角形,且侧面
底面
,E为线段
的中点,M在线段
上.
![](https://img.xkw.com/dksih/QBM/2021/5/20/2725201910865920/2726315748270080/STEM/e9c6c927-4045-4981-b07c-61928b3fca9c.png?resizew=293)
(1)求证:
;
(2)当点
满足
时,求多面体
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e075468e7fb0bf30229aec01a7205977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://img.xkw.com/dksih/QBM/2021/5/20/2725201910865920/2726315748270080/STEM/e9c6c927-4045-4981-b07c-61928b3fca9c.png?resizew=293)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bc56fdf70e65bd88980c64af96b83da.png)
(2)当点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/515cbd4812397175980507ca44572c3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d231b17c5992eee495184b0eae66749.png)
您最近一年使用:0次
2021-05-22更新
|
793次组卷
|
3卷引用:重庆市缙云教育联盟2022-2023学年高一下学期期末数学试题
重庆市缙云教育联盟2022-2023学年高一下学期期末数学试题陕西省宝鸡市千阳中学2021届高三下学期第四次适应性训练文科数学试题(已下线)专题01 立体几何求体积-【解题思路培养】2022年高考数学一轮复习解答题拿分秘籍(全国通用版)
5 . 如图,在多面体ABCDE中,
,
平面ABC,
,
,
,F为BC的中点,且
.
(1)求证:
平面ADF;
(2)求多面体ABCDE的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9d7bd6df0e94731edb8f4649903de73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97f30533da2e1d2a958dc906c37eba9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e405b53cf66f14c54e9ae1e2a013f5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dc9795efa99b6fb9fdf9778085dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecf7679c8b4b1e442ce4286d4b0e9c32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/508f8d607c633e9b008d48ac3dcd22e2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/17/1b918c3b-eb0b-4714-8cea-a74d779d4793.png?resizew=135)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a5f445af1ae136773cb338920552ff2.png)
(2)求多面体ABCDE的体积.
您最近一年使用:0次
2020-02-24更新
|
232次组卷
|
2卷引用:重庆市第八中学2018-2019学年高二上学期期末(文)数学试题
6 . 如图,四边形
是等腰梯形,
,
,
,在梯形
中,
,且
,
平面
.
(1)求证:平面
平面
;
(2)若二面角
的大小为
,求几何体
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0fff774b4b0087a6f304ce930d359be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e075468e7fb0bf30229aec01a7205977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58ea8ab3d191cebcb69e087f7b3263ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd4b93d7abcfc4c3df48f03aa969c17f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68dfd32a77c3615069ad1e7eb5b226a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3471bde9ec2c95cc301b4b3f468ca4aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f09ad78d4eccd1a9c9ccd3c4af79c79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e02b6df2041ef74bd8a80c9f1ab7cf47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1077520a4816bbb5a37fc45359e34c5c.png)
(2)若二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5680c88274fe3de009b76721b1128e0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20b69099d2b74ffbb1f365e1468bd8fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/17/dd31f439-617e-4b56-8166-1a1c8d2b2d5c.png?resizew=133)
您最近一年使用:0次
2018-02-09更新
|
503次组卷
|
2卷引用:重庆市第一中学2017-2018学年高二上学期期末考试数学(理)试题