解题方法
1 . 如图一,将边长为2的正方形
剪去四个全等的等腰三角形后,折成如图二所示的正四棱锥.记该正四棱锥的斜高为
(侧面三角形的高),
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/7/821276de-d4d7-4f18-a24e-658a6bde1412.png?resizew=244)
(1)求证:
;
(2)将折起来后所得正四棱锥的表面积记为
,请将
表示为
的函数,并求
的范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80b53eab97158937f92039c1e133b0f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/535020bea3472a6ef9f0256bd37ccbc3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/7/821276de-d4d7-4f18-a24e-658a6bde1412.png?resizew=244)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c04e8a297b28f18d198206a60501996a.png)
(2)将折起来后所得正四棱锥的表面积记为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
您最近一年使用:0次
解题方法
2 . 在三棱台
中,
平面ABC,
,
,
,M为AC的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/7/76e196e5-dae0-4806-abbd-d5abf35695ea.png?resizew=181)
(1)证明:
平面
;
(2)若
,求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1ecf072589c0f901d92f6bda111d841.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bd46192ef38736d992bf2b330b07bfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea937da23eb3b8ae2affe2fa41ca085b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/7/76e196e5-dae0-4806-abbd-d5abf35695ea.png?resizew=181)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d1d2e0f281222a5f289ea4008370aed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de9078475c350c04bd97666d808dd55a.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f54638dd4ebf19815a1333d84e42f927.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de9078475c350c04bd97666d808dd55a.png)
您最近一年使用:0次
名校
3 . 如图,在正方体
中,点
,
分别在棱
,
上,且满足
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/1/0fa3319b-d01d-4cd7-abcb-78ccd815b406.png?resizew=158)
(1)证明:平面
平面
;
(2)若
,求平面
截正方体
所得截面的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62ce78060fece67bbb0a387d06757f51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84f31a3724c639f88486f8356ca65397.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/1/0fa3319b-d01d-4cd7-abcb-78ccd815b406.png?resizew=158)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d28c625d7ac6878957facc8274d459c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/882bc11eba4f28780fc0d928ead2dbbc.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efc6e4b936d7a800e839a30c3839574d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ee076fe7dbca5616c4e8a6869a355f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
您最近一年使用:0次
2019-12-12更新
|
320次组卷
|
3卷引用:贵州省贵阳市2019-2020学年高二上学期联合考试数学(文科)试题