某养殖场建造圆锥形仓库用于贮藏玉米,已建的仓库的底面直径为16
,高6
,现准备建一个更大的圆锥形仓库,以存放更多的玉米,有两种方案:一是新建的仓库的底面直径比原来大4
(高不变);二是高增加
(底部直径不变).
(1)分别计算按这两种方案所建的仓库的体积;
(2)分别计算按这两种方案所建的仓库的侧面积;
(3)判断哪个方案更经济些.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e15e00f40396e914d1d9955bd7785f1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e15e00f40396e914d1d9955bd7785f1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e15e00f40396e914d1d9955bd7785f1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff47258bb60823c4d84ce19503c96a56.png)
(1)分别计算按这两种方案所建的仓库的体积;
(2)分别计算按这两种方案所建的仓库的侧面积;
(3)判断哪个方案更经济些.
更新时间:2021-08-14 08:40:06
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【推荐1】过圆锥轴的截面为等腰直角三角形
,
为底面圆周上一点,已知
,圆锥体积为
,点
为底面圆的圆心
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/11/39d528ba-1be0-4fec-b1e7-abda4a03ef68.png?resizew=197)
(1)求该圆锥的全面积
(2)求异面直线
与
所成角的大小(结果用反三角函数表示)
(3)求点
到平面
的距离
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc9c9cfa597b444b5c9dbae7a825a695.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/11/39d528ba-1be0-4fec-b1e7-abda4a03ef68.png?resizew=197)
(1)求该圆锥的全面积
(2)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a6e2867f32d3f1c3cd36cd3a11a8580.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb6ede9761b5b90f8dc137708e1ee90f.png)
(3)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edca7e25845429d727381e9e80024aa0.png)
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解答题-问答题
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【推荐2】在
中,AB=6,AC=8,BC=10.
(1)求将
绕AB所在的直线旋转一周所得的几何体的体积;
(2)求将
绕BC所在的直线旋转一周所得的几何体的表面积.
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(1)求将
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e428e7a09732be85c1224e9c8f6a71c5.png)
(2)求将
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e428e7a09732be85c1224e9c8f6a71c5.png)
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解答题-证明题
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解题方法
【推荐1】如图,三棱柱
中,侧面
底面
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,
,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/25/da363c51-0311-451b-9b85-b28e883585af.png?resizew=211)
(1)求证:
;
(2)求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0671b4776e142e17a79af5b3f0378ef7.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3570a95f68349fcd9417fcda62e78e7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/25/da363c51-0311-451b-9b85-b28e883585af.png?resizew=211)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fd38f4fd6af2418573bcc7b67119be5.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/591831427c5a4501c84bab22993211da.png)
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解答题-问答题
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(0.85)
解题方法
【推荐2】如图,在三棱锥
中,
,
,O为棱AC的中点.
![](https://img.xkw.com/dksih/QBM/2022/7/1/3013237568692224/3014442459144192/STEM/0df85cc4f66942289b322502b0037232.png?resizew=226)
(1)证明:
平面
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(2)若点M在被AB上,且A到平面POM的距离为
,求平面POM将三棱锥
分成的左、右两部分的体积之比.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b370b7ca2390e41f13ccf2217fc85071.png)
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![](https://img.xkw.com/dksih/QBM/2022/7/1/3013237568692224/3014442459144192/STEM/0df85cc4f66942289b322502b0037232.png?resizew=226)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3e126c16032892966489053f44b9048.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)若点M在被AB上,且A到平面POM的距离为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
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