如图,已知圆
的半径为
,点
在直径
的延长线上,
,点
是圆
上半圆上的一个动点,以
为斜边做等腰直角三角形
,且
与圆心分别在
两侧.
![](https://img.xkw.com/dksih/QBM/2022/11/9/3105805454598144/3106149012086784/STEM/5dd05ea62a994ee78281510bfe1f0d6e.png?resizew=154)
(1)若
,试将四边形
的面积
表示成
的函数;
(2)求四边形
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa7aeb2a8d1437eeb4482c3b6ad9f315.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://img.xkw.com/dksih/QBM/2022/11/9/3105805454598144/3106149012086784/STEM/5dd05ea62a994ee78281510bfe1f0d6e.png?resizew=154)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/259728433d68902065408fb6a34c6d4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4af2b217f3d432178546e8ece720c220.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
(2)求四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4af2b217f3d432178546e8ece720c220.png)
更新时间:2022-11-09 22:19:15
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解题方法
【推荐1】某公司要在一条笔直的道路边安装路灯,要求灯柱
与地面垂直,灯杆
与灯柱
所在的平面与道路走向垂直,路灯
采用锥形灯罩,射出的光线与平面
的部分截面如图中阴影部分所示.已知
,路宽
米.设![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa278e0c5e5bd37ca1ea88871da0293f.png)
![](https://img.xkw.com/dksih/QBM/2022/11/27/3118579942170624/3119494008872960/STEM/9d5162e9a86a448a90527af543ce805e.png?resizew=218)
(1)求灯柱
的高
(用
表示);
(2)此公司应该如何设置
的值才能使制造路灯灯柱
与灯杆
所用材料的总长度最小?最小值为多少?(结果精确到
米)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e77fdec7285f827f4b788c7dd44bbefb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcf05aaa351239448a9ab0e048f76faf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa278e0c5e5bd37ca1ea88871da0293f.png)
![](https://img.xkw.com/dksih/QBM/2022/11/27/3118579942170624/3119494008872960/STEM/9d5162e9a86a448a90527af543ce805e.png?resizew=218)
(1)求灯柱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eabd5f3a86afe49dcd70571e2b96cfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
(2)此公司应该如何设置
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e2c4d12b3a705daab723ab243b6cc88.png)
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【推荐2】如图所示,
是圆锥的一部分(A为圆锥的顶点),
是底面圆的圆心,
,
是弧
上一动点(不与
、
重合),满足
.
是
的中点,
.
![](https://img.xkw.com/dksih/QBM/2022/2/10/2913473877712896/2921446104268800/STEM/dd013b3a-2267-4654-8cdc-88b6edd2d93f.png?resizew=136)
(1)若
平面
,求
的值;
(2)若四棱锥
的体积大于
,求三棱锥
体积的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad7d022859b8853d7be8f2bf6487a693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8026ad627e8ae6c4acb9140a02181f29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21b710be34d39a3058bad08e397849e4.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/5811e450dcff0e190c3d7378c08797c5.png)
![](https://img.xkw.com/dksih/QBM/2022/2/10/2913473877712896/2921446104268800/STEM/dd013b3a-2267-4654-8cdc-88b6edd2d93f.png?resizew=136)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3123da0313d458c833e82aaa234b9117.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ed01d1ff5a7f21a68fb3a1e5c7f393e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de7d5ef3a3d9a03be91135fc426d57cc.png)
(2)若四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f28ba8a560e3b54f9346f2a6a805c016.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56d266a04f3dc7483eddbc26c5e487db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40cc229e0951e5d141f3c8341d17c593.png)
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【推荐3】为落实《中共中央、国务院关于全面加强新时代大中小学劳动教育的意见》,加快构建德智体美劳全面培养的教育体系,开齐、开足、开好德育、体育、美育、劳动教育课程,某校成立了劳技兴趣小组.为了迎接“五一”晚会,该小组制作了一个半径为
的圆形灯箱,其发光部分为该圆内的一个关于圆心对称的“工”型,“工”型由横、竖、横三个等宽的矩形组成,两个横向矩形全等且它们的长边是竖直矩形的长边的
倍,设
为圆心,
,“工”型的面积记为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/19/e92afeea-f79a-494c-87d6-71cd6a10f327.png?resizew=148)
(1)将
表示为
的函数;
(2)为了使得灯箱亮度最大,设计时应使
尽可能大,则当
为何值时,
最大?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1865d71d450db8e7d41d29874dd7c295.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/19/e92afeea-f79a-494c-87d6-71cd6a10f327.png?resizew=148)
(1)将
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
(2)为了使得灯箱亮度最大,设计时应使
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
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【推荐1】如图所示,某镇有一块空地
,其中
,
,
.当地镇政府规划将这块空地改造成一个旅游景点,拟在中间挖一个人工湖
,其中
都在边
上,且
,挖出的泥土堆放在
地带上形成假山,剩下的
地带开设儿童游乐场.为安全起见,需在
的周围安装防护网.
时,求防护网的总长度;
(2)若要求挖人工湖用地
的面积是堆假山用地
的面积的
倍,试确定
的大小;
(3)为节省投入资金,人工湖
的面积要尽可能小,问如何设计施工方案,可使
的面积最小?最小面积是多少?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a29ac2834e2f2f1c32149fe31f107134.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fd446f72000300a54fb9e1e28325093.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9e21aa38de80da8ccaa7ce51595e7bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25dd698d57d1cf239eb8752aecaaa4f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c3fe26b378cb2665c06c5d8039d675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0edafce95aade0386bc0d78f679dcf47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caf2b5e712b42f748a3c30bb5d160c18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c29e963e1871b415c086bc600d16bd5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc8a5801b87418e955e5d8b5f785b090.png)
(2)若要求挖人工湖用地
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25dd698d57d1cf239eb8752aecaaa4f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0edafce95aade0386bc0d78f679dcf47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f92f279be7c8a11dcd2c0a97116bdcbb.png)
(3)为节省投入资金,人工湖
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25dd698d57d1cf239eb8752aecaaa4f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25dd698d57d1cf239eb8752aecaaa4f4.png)
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【推荐2】已知在锐角
中,
,
,
为角
,
,
所对的边,且
.
(1)求角
的值;
(2)若
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4179570a06383d6bad862dc02d2a8d8.png)
(1)求角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8120119749d4bc28067e73fca7d46cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5cbff84327e964f912a54032e76ccc9.png)
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