名校
解题方法
1 . 如图,在四棱锥
中,底面
是边长为1的正方形,
底面
,
,点
是棱
的中点.
![](https://img.xkw.com/dksih/QBM/2021/7/25/2772004297392128/2784664253194240/STEM/155d8f18-58b0-4179-b5fa-aa5310d6eb70.png?resizew=262)
(Ⅰ)求证:
平面
;
(Ⅱ)求三棱锥
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/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/829f9180ddd9aa1a0ee0dc520f4e0b5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://img.xkw.com/dksih/QBM/2021/7/25/2772004297392128/2784664253194240/STEM/155d8f18-58b0-4179-b5fa-aa5310d6eb70.png?resizew=262)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30067b7b236d17af8a462f96a58d11bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af68a7bf0da4f7c6f739d2e2461ad9b7.png)
(Ⅱ)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9bad875ab4b5b8c707d452db4cabaa4.png)
您最近一年使用:0次
2 . 若一个圆锥的高和底面直径相等,且它的体积为
,则此圆锥的侧面积为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44917f942c3fd36614f58d47b5fe1821.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2021-07-23更新
|
1113次组卷
|
4卷引用:吉林省松原市长岭县第三中学2020-2021学年高一下学期第七次月考数学试题
名校
解题方法
3 . 如图,在直三棱
中,点
是棱
的中点,
,
.
![](https://img.xkw.com/dksih/QBM/2021/7/13/2763378167824384/2766899290513408/STEM/298ac327-fffd-4791-adb4-ec9e79748aab.png?resizew=200)
(1)求证:
平面
;
(2)若
是
的中点,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98e486a1aad96167ff62f6fb5136e0bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29e5a6afab22d5b53c1d8e87d58e8020.png)
![](https://img.xkw.com/dksih/QBM/2021/7/13/2763378167824384/2766899290513408/STEM/298ac327-fffd-4791-adb4-ec9e79748aab.png?resizew=200)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02cb62f4c1e0e023619922eb8a509c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7935fe3125f247b7bea4f065ce9ad985.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb49fdc6b6bbb2449fdf8a0de769d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6e18b1118152ed4cb68cf6c8c7fdece.png)
您最近一年使用:0次
2021-07-18更新
|
329次组卷
|
2卷引用:吉林省松原市长岭县第三中学2020-2021学年高一下学期期末数学试题
4 . 如图,四边形
是矩形,
平面
,
平面
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/1c2c8a53-888c-4bfc-a2d6-1f947451920c.png?resizew=173)
(1)证明:平面
平面
.
(2)求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7a38e6c6dfde2b19b6b47f35a439a06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b1d3de310412c0fa445acd2cdb61513.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f8eeeea1c9652cacce976f8129cf520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71e4c7f120dc750a40193df735d73243.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/1c2c8a53-888c-4bfc-a2d6-1f947451920c.png?resizew=173)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e623816106bf7ef00fdb597f53c23ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a09d9d486b7f91ba933210dd013a7f2c.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/209e3b87346e057276f0692a7361e446.png)
您最近一年使用:0次
2021-07-08更新
|
960次组卷
|
5卷引用:吉林省松原市实验高级中学2020-2021学年高一下学期期末数学试题
5 . 已知一个圆柱的侧面积等于其表面积的
,且其轴截面的周长为24,则该圆柱的体积为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf31876698721a199c7c53c6b320aa86.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2020-08-03更新
|
828次组卷
|
4卷引用:吉林省松原市实验高级中学2020-2021学年高一下学期期末数学试题
6 . 如图,四棱柱ABCD-A1B1C1D1的底面ABCD是正方形,O为底面中心,A1O⊥平面ABCD,AB=AA1=
.
![](https://img.xkw.com/dksih/QBM/2019/1/9/2115117509525504/2117053779369984/STEM/6c545ecc-8a2b-428e-b762-113627af8370.png)
(1)证明:
;
(2)
;
(3)求三棱柱ABD-
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://img.xkw.com/dksih/QBM/2019/1/9/2115117509525504/2117053779369984/STEM/6c545ecc-8a2b-428e-b762-113627af8370.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/035079fea1677164e49ab975c8287bb2.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff1980a084dbd230602628b174075ecb.png)
(3)求三棱柱ABD-
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3897359e55f0cfb8620d4f7b864ddbc.png)
您最近一年使用:0次
7 . 如图,将边长为1的正方形ABCD沿对角线AC折起成直二面角D-AC-B,在折起后形成的三棱锥D-ABC中,给出下列三个命题:①△DBC是等边三角形;②异面直线AC与BD成
;③三棱锥C-ABD的体积是
;④三棱锥D-ABC的表面积是1+
;⑤AD与平面ABC所成角为45°其中正确命题的序号是
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/31/96b1dd71-69d9-45ff-accb-86c084daa8c6.png?resizew=204)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6714cb03742e6c67e4d00b90e8f4c8a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0467b0675c3ecfb282cc88255284d3e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/31/96b1dd71-69d9-45ff-accb-86c084daa8c6.png?resizew=204)
A.①② | B.②③④ | C.①②④⑤ | D.①②③④ |
您最近一年使用:0次
名校
8 . 如图,在三棱锥
中,
,平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
平面
,
、
分别为
、
的中点.
(1)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
平面
;
(2)求证:
;
(3)求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbf14ca7749296b3fa703ea85fe73123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1633988fd62a652de726ee92a917b52d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895d6f710d5f67e1d4c7408d50d77281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f45265eaed2ba5fc08f6a112a02cd2.png)
(3)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ba5dac1a0e472a507c73832dd4ef6e5.png)
![](https://img.xkw.com/dksih/QBM/2018/1/29/1870650111180800/1873711218786304/STEM/0e535e5abcd0443eb3cea9c2bba86876.png?resizew=143)
您最近一年使用:0次
2018-02-02更新
|
1217次组卷
|
7卷引用:【校级联考】吉林省扶余市第一中学2018-2019学年高一上学期期末考试数学试题
9 . 在正方体
中,直线
与平面
所成的角的余弦值等于( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7935fe3125f247b7bea4f065ce9ad985.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
10 . 某几何体的三视图如图所示,则该几何体的体积等于
![](https://img.xkw.com/dksih/QBM/2017/5/12/1685504240549888/1686039683588096/STEM/4095ab42-b171-4375-8c0f-eaa9b7adb092.png?resizew=267)
![](https://img.xkw.com/dksih/QBM/2017/5/12/1685504240549888/1686039683588096/STEM/4095ab42-b171-4375-8c0f-eaa9b7adb092.png?resizew=267)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2017-05-13更新
|
924次组卷
|
3卷引用:吉林油田高级中学2019-2020学年第二学期高一期末考试数学(理)试题