解题方法
1 . 某箱子的容积与底面边长
的关系为
,则当箱子的容积最大时,箱子底面边长为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/435c3b5983b230540c99dd6e58162d5b.png)
A.![]() | B.![]() | C.![]() | D.其他 |
您最近一年使用:0次
解题方法
2 . 将一个边长为
米的正六边形铁皮的六个角截去六个全等的四边形,再把它沿虚线折起(如图),做成一个无盖的正六棱柱铁皮盒.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/21/7bdec23b-a760-42cd-b4be-adc4a9d9c0f6.png?resizew=307)
(1)试把这个正六棱柱铁皮盒的容积
表示为盒底边长
的函数;
(2)
多大时,盒子的容积
最大?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/21/7bdec23b-a760-42cd-b4be-adc4a9d9c0f6.png?resizew=307)
(1)试把这个正六棱柱铁皮盒的容积
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be54e84508decfcce6d2fcbe6c8c1a92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be54e84508decfcce6d2fcbe6c8c1a92.png)
您最近一年使用:0次
19-20高二下·江苏苏州·期中
解题方法
3 . 如图是一个钻头的示意图,上部是一个圆锥
,下部是一个圆柱
,圆锥的底面与圆柱的上底面重合,圆锥的底面半径
和高
以及圆柱的高
都可以调节其大小.已知圆锥的母线长为定值
,且
.设钻头的体积为
,圆锥的侧面积为
.
![](https://img.xkw.com/dksih/QBM/2021/3/12/2676156051292160/2676297783623680/STEM/37ba5079-52f4-4cc4-9ff1-d277038215b4.png)
(1)试验表明:当且仅当
取得最大值时,钻头的冲击力最大.试求冲击力最大时,
分别为多少;
(2)试求钻头的体积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e65ac334119ccd6204402a7aba29a55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3711953485a76de370a04756009a644a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eabd5f3a86afe49dcd70571e2b96cfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff778eda45985fdd877c55fad959af51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be54e84508decfcce6d2fcbe6c8c1a92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://img.xkw.com/dksih/QBM/2021/3/12/2676156051292160/2676297783623680/STEM/37ba5079-52f4-4cc4-9ff1-d277038215b4.png)
(1)试验表明:当且仅当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ba9638ee1a002ea8ba393eefd876c57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1960fa68fec9bbf4779e70c80de02d0d.png)
(2)试求钻头的体积的最大值.
您最近一年使用:0次
名校
解题方法
4 . 如图,圆柱体木材的横截面半径 为
,从该木材中截取一段圆柱体,再加工制作成直四棱柱
,该四棱柱的上、下底面均为等腰梯形,分别内接于圆柱的上、下底面,下底面圆的圆心
在梯形
内部,
,
,
,设
.
![](https://img.xkw.com/dksih/QBM/2020/3/11/2417240916082688/2419505826234368/STEM/8cfd3f3d350d4cfcb83a11e98c9ada03.png?resizew=142)
(1)求梯形
的面积;
(2)当
取何值时,直四棱柱
的体积最大?并求出最大值(注:木材的长度足够长)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc3b99ebc9981bcd5cecf799717b8e9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10df84d553a8826a7ce9bff4bf0d95b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea4f5eec0addba78f2e0cdfb7ecc59a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73e0aa7d7faf508bacfd7fa5ae00affb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e6837f98456e149998d1ade17f0946c.png)
![](https://img.xkw.com/dksih/QBM/2020/3/11/2417240916082688/2419505826234368/STEM/8cfd3f3d350d4cfcb83a11e98c9ada03.png?resizew=142)
(1)求梯形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de7d5ef3a3d9a03be91135fc426d57cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
您最近一年使用:0次
解题方法
5 . 从边长为
的矩形纸板的四角截去四个相同的小正方形,作成一个无盖的盒子.盒子的高为多少时,盒子的容积最大?最大容积是多少?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afcca4b7496fe86dba77d4ff1b5bce6b.png)
您最近一年使用:0次
2016-12-04更新
|
201次组卷
|
2卷引用:2015-2016学年江苏连云港东海县房山高级中学高二下期中文数学试卷