1 . 现需要设计一个仓库,由上、下两部分组成,上部的形状是正四棱锥
,下部的形状是正四棱柱
(如图所示),并要求正四棱柱的高
是正四棱锥的高
的4倍.
,
,则仓库的容积是多少?
(2)若正四棱锥的侧棱长为
,
,则正四棱锥
的侧面积是多少?
(3)若正四棱锥的侧棱长为
,当
为多少时,下部的正四棱柱侧面积最大,最大面积是多少?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724625d4f91f0e48712d6d143a6389b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae0a4f38420bb9215dbc9c875b755838.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32fb50c66cd2de786b39cb442ec54a16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49caee3119b29a99e62cbe419fb261fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c67c2eb45b423807aa39632e0d25fbfe.png)
(2)若正四棱锥的侧棱长为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e17ee14bd91bfff409c06fd434f6745.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c67c2eb45b423807aa39632e0d25fbfe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724625d4f91f0e48712d6d143a6389b7.png)
(3)若正四棱锥的侧棱长为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e17ee14bd91bfff409c06fd434f6745.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32fb50c66cd2de786b39cb442ec54a16.png)
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名校
解题方法
2 . 在
中,角
的对边分别为
,且
.
(1)求
的值;
(2)若
为锐角三角形,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d78340a3105486043276458198f548f6.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b32f2d4d1d2c16c54b2caef17840bfcb.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9ecc3aaae2aa289591a3b632f1e0645.png)
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3 . 函数
在区间
上的最大值为6.
(1)求常数m的值;
(2)把函数
的图象上各点向右平移
个单位长度得到函数
,求
的值;
(3)当
时,求函数
的最小值,以及相应x的集合.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15ef71756ef8bfae1442a859d0a60392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff14bdd7f2b48c0ce6ba8696c89fbf68.png)
(1)求常数m的值;
(2)把函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c8ae071199874d9d74a4919a58902f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c59e8a5ef964f0eb31e107575fd07a7.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb63478132d4c1fef3c17e591919da83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
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解题方法
4 . 如图,底面边长为2且侧棱长为
的正六棱锥
是底面的中心,在其内部有一个高为
的内接圆柱(圆柱的下底面在棱锥的底面上,上底面圆周与棱锥各侧面相切).
(2)求圆柱侧面积的最大值及侧面积取得最大值时圆柱底面半径的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fed9d3330335f4989018db5397a146d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)求圆柱侧面积的最大值及侧面积取得最大值时圆柱底面半径的值.
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解题方法
5 . 古希腊的数学家海伦在其著作《测地术》中给出了由三角形的三边长a,b,c计算三角形面积的公式:
,这个公式常称为海伦公式,其中,
.我国南宋著名数学家秦九韶在《数书九章》中给出了由三角形的三边长a,b,c计算三角形面积的公式:
,这个公式常称为“三斜求积”公式.
(1)已知
的三条边分别为
,求
的面积;
(2)利用题中所给信息,证明三角形的面积公式
;
(3)在
中,
,求
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/684c13a2cea962fb204256ca433a4d58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71d788614f1841b4943b30fe6fd1eff3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ad209824da2aadcf7b5479de68187cc.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51ed8dab1f54de9e1fc65fb53600610c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(2)利用题中所给信息,证明三角形的面积公式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/634fdb49ecc32befaf9ac4ce84ae5a37.png)
(3)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b0eba33aa912c5ce4be622945b0243c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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解题方法
6 . 在锐角
中,角
,
,
的对边分别为
,
,
,已知
.
(1)求
;
(2)若
的面积为
,求
,
;
(3)若
,求
周长的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.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/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/3de9ff601d4e299c50cd2fc7c6923087.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c822e13da88844e7dcc02ecd4ec55e52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adbd3e8cf8325999cde03adf845d3dd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6de1d395e6c48c0676a1488a299479d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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解题方法
7 . 设
是虚数,
(1)若
是实数且
,求
的实部的取值集合;
(2)若
是关于
的方程
的一个根,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af68f652b4c13657ffddf3c9e7eb262b.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/174ce5fa8bd9b7c64f634c73f8e1c238.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56bd60194534e5488f4a2fb2dd34d63d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af68f652b4c13657ffddf3c9e7eb262b.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f39b7e466956e27b579ff6013496be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a21f9f057ed61c18f1e016da2df4656.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af68f652b4c13657ffddf3c9e7eb262b.png)
您最近一年使用:0次
8 . 祖暅在求球体积时,使用一个原理:“幂势既同,则积不容异”.“幂”是截面积,“势”是立体的高.意思是两个同高的立体,如在等高处的截面积恒相等,则体积相等.更详细点说就是,界于两个平行平面之间的两个立体,被任一平行于这两个平面的平面所截,如果两个截面的面积恒相等,则这两个立体的体积相等.上述原理在中国被称为祖暅原理.如图是一个半径为
的球体,平面
与球相交,截面为圆
,延长
,交球于点
,则
垂直于圆
(
垂直于圆
内的所有直线).
,求圆锥DB的表面积和体积;
(2)如图平面
上方与球体之间的部分叫球冠,若
,请你利用祖暅原理求球冠的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf1438142deeac876fc7dc50552e552.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf1438142deeac876fc7dc50552e552.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf1438142deeac876fc7dc50552e552.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0be901bc31043f90194eb4131bf22b00.png)
(2)如图平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a6c9414983f9771bbb06bf9a3e75f8d.png)
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解题方法
9 . 在
中,角
,
,
的对边分别为
,
,
,且
.
(1)求角
的大小;
(2)若
,
,且
,求
边上中线的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.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/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/9906f270537d07492730f7856b3d42bb.png)
(1)求角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4313d6184e087fa6753a02379a8f8a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8120119749d4bc28067e73fca7d46cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d5556dd86322752a457b3a6ba979c80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
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10 . 已知向量
,
,函数
.
(1)求函数
的最小正周期及单调递增区间;
(2)已知
中,内角A,B,C所对的边分别为a,b,c且满足
,如图.
,求
的面积;
(ⅱ)若
,
,
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a504b887b7f9c75abb28638a21576e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cda109e624deb07ed136f953825becef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98a89b44ca16560866b50a4602b4e6f8.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3869f7181ef61b495e3f506cd7cbd1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/084efe0832c94e5fac28b7acf2487595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a5eacc284e5ed2e19dd0aaa585a31c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b766c01f65ed08eb62f94d55220dd849.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f66c2c239799b7f11f9a971a807f8d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fabb884dc5f9609de491245463bbe9a.png)
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