解题方法
1 . 在四面体
中,
为
中点,
为
外接球的球心,
.
(1)证明:
;
(2)若
,求四面体
体积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a351136b18bc7d3bd5122332772ab23b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a351136b18bc7d3bd5122332772ab23b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0398ca118304f21b6fc3c36ecf8bf2f4.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab17db0e6518d617247e17afd313a6a2.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/578b12f739ef7fc54c65b8435b3c16aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af286347445bc77ba5dc6efb5fcc5b8f.png)
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名校
2 . 如图,
为圆柱
的一条母线,且
.过点
且不与圆柱底面平行的平面
与平面
垂直,轴
与
交于点
,平面
截圆柱的侧面得到一条闭合截线,截线与平面
的另一交点为
.已知该截线为一椭圆,且
和
分别为其长轴和短轴,
为其中心.
为
在上底面内的射影.记椭圆的离心率为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/8/892a49ce-b069-47b8-afe1-3e8c0f767d7c.png?resizew=201)
(1)证明:
,并求
的取值范围;
(2)当
时,求直线
与平面
所成的角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9399c9a2a31b0e3165aea2d6ccc4f7c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e65ac334119ccd6204402a7aba29a55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97e4b7fca8edf790c85f789a713d0f2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57972bfc01ddc7ab9535ed5b9bcbc3ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e65ac334119ccd6204402a7aba29a55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57972bfc01ddc7ab9535ed5b9bcbc3ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/473913c0887bb64d386f4c02f1853452.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bc9076974ebd6331d67055302be8167.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a71fc9c0068109dad1382354570665.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/8/892a49ce-b069-47b8-afe1-3e8c0f767d7c.png?resizew=201)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e74ab7abb97717abd4f75e09805e219.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd38f55d7cdae1de6e2a2e2c6e1e57d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
您最近一年使用:0次
2023-02-01更新
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564次组卷
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3卷引用:“加速杯”新高考2023届高三一月迎新春调研测试数学试题