名校
1 . 如图,在四棱锥
中,底面
是平行四边形,
分别为
的中点,
为线段
上一点,且
.
平面
;
(2)若四棱锥
为正四棱锥,且
,求四棱锥
的外接球与正四棱锥
的体积之比.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e7344dca1e40bf072371ddd5640111.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e96d954fad9d528c69a21129837431cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b8badfeb9e7556486e02ab60df4dd32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4734735213b599a9915e1ed91a5d8ce4.png)
(2)若四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9d5d99f272872783fce8189096298d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
您最近一年使用:0次
2024-06-17更新
|
702次组卷
|
2卷引用:福建省福州市部分学校教学联盟2023-2024学年高一下学期期末模拟考试数学试题
名校
2 . 如图,在四棱锥
中,
面
,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/4/ff989604-a9bb-454d-8888-c995f4a9c305.png?resizew=161)
(1)求三棱锥
内切球的体积.
(2)求平面
与平面
的夹角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80c66c71528ef937fdfc7c80798c46b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca9a222b416eb9cdd0cc26119707b3f5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/4/ff989604-a9bb-454d-8888-c995f4a9c305.png?resizew=161)
(1)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
您最近一年使用:0次
3 . 上海中心大厦是上海市的地标建筑,现为中国第一高楼.为有效减少建筑所受的风荷载,通常对建筑体型进行一定的扭转.上海中心大厦的主楼可近似看成将正三棱柱的一个底面扭转所得的几何体;将正三棱柱
的底面
在其所在平面内绕
的中心逆时针旋转
得到
,再分别连接
、
、
、
、
、
所得的几何体.已知大厦的主楼高度约为
米,底层面积(即
的面积)约为
平方米.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/31/fdf3aa87-7bc9-4fc4-a1b2-d692595b7966.png?resizew=149)
(1)求证:
;
(2)试分别以正三棱柱
和几何体
为模型估算大厦主楼的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4310db23fc79936c7182361e652bab1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4310db23fc79936c7182361e652bab1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d5bca00fa20e6e80480b9d06d2e52ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8ee6e1d480ece7117e1f87ebf4bbeea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f986a0d8f37177dcccfee3898a66fd00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e663220a66eff19da6a71e46b397db2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20c431cd12f858f0bc8dabb1d8c0b8e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/020ebe1219437129358b986eb9e70bbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/300d29bf2277a510ab443c1e2a55e1bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4336253885d52e43ba6eaa297ea847b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3157362e4455a2176539f8bdcfcea93c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2faca11afa8ddaa19cde2e91ee5983f7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/31/d2649820-fc38-45b9-ba26-9032c8bf3c25.jpg?resizew=128)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/31/fdf3aa87-7bc9-4fc4-a1b2-d692595b7966.png?resizew=149)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/154c43b58f7f6389d6d71aa520b6c34f.png)
(2)试分别以正三棱柱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71f2185273bf04c11118c7954f7ec822.png)
您最近一年使用:0次
4 . 如图,在四棱锥
中,底面
为梯形,平面
平面
,
,
,
是等边三角形,O,M分别为线段AB,PB的中点,且
,
.
(1)求证:
平面
;
(2)求多面体
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f79863ffcfa63117ca6741b20a48e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6de3595bb7c79503fabd75d99196ccb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/3/392ce3dd-5880-43b9-8b70-e2877e9b3ecd.png?resizew=161)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5865d488a9cf1181016fd2e866177cdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)求多面体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1b05fa47289b0164d51d9585464ce9a.png)
您最近一年使用:0次
名校
5 . 已知圆锥的顶点为
,
为底面圆心,
,异面直线
与
所成角的余弦值为
,
的面积为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/12/6282a5fe-9f1b-4ba2-9b49-9c65dbb578de.png?resizew=147)
(1)求该圆锥的表面积;
(2)求该圆锥内半径最大的球的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/950e673dc286ecdfa54dc7ab146770b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a6e2867f32d3f1c3cd36cd3a11a8580.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e6486784415f3537c9a13556c05d893.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72e49817548cb45b3d1e58570644c6fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/461dc722a8b3edc8147bf7b5f6e6eb11.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/12/6282a5fe-9f1b-4ba2-9b49-9c65dbb578de.png?resizew=147)
(1)求该圆锥的表面积;
(2)求该圆锥内半径最大的球的体积.
您最近一年使用:0次
2023-12-12更新
|
222次组卷
|
2卷引用:江西省赣州市南康中学2024届高三上学期"七省联考"考前数学猜题卷(十)
解题方法
6 . 如图,在多面体
中,
是四边形
的外接圆的直径,
是
与
的交点,
,
.四边形
是直角梯形,
,
平面
,
.
(1)求证:
平面
;
(2)求多面体
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e735a28578ba191da6d4f3b0f8e8729.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5640c531110986a503de677715770e62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ecc1cb55a57dde481f8dd07ab150676.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8139d9fd5c670c91aa7dc485366dd1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8d2d217e9bcd059908f117dfc4d4259.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4592d3d223b4f8c93c9308afadfa79b3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/3/ba2c66a8-559a-42e7-950a-89bb8b177514.png?resizew=133)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8197bf06d017950c85c3ba6a291c095e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c0bfeadcf17b2a45896071f07a4a5a.png)
(2)求多面体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
您最近一年使用:0次
解题方法
7 . 如图I为某同学搭建的立体几何模型,相关性质如图描述,其侧面展开图如图II所示.图I中,圆锥
的半径为3,体积为12π. 在等腰
(可近似看作与扇形KUN重合)中,
.中间圆柱展开图可看作正方形.圆柱J-G中,半径为3,体积为45π.侧面非阴影部分的圆边共占20%.设圆O所在平面为
,圆G所在平面为
,各立方体平稳放置,回答以下问题:
.
(2)试求K到G的距离及阴影部分面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/181928a80db33cfb7b903f50ebad01f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c27f6dcfcbc956cab53d53f39d5c47d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c11a3684becedd099419cc3fc019373.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce52a7419783b3542d19b755e2cb028d.png)
(2)试求K到G的距离及阴影部分面积.
您最近一年使用:0次
解题方法
8 . 如图,在正四棱柱
中,
,
∥平面MAC.
(1)证明:M是
的中点;
(2)若正四棱柱的外接球的体积是
,求该正四棱柱的表面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92535536bd3c2761724fd058427f95a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fe734023d4e70010a6b2cc3267cb86e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/5/e7673eec-8fe4-47f5-a514-8bc8c82a4303.png?resizew=125)
(1)证明:M是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
(2)若正四棱柱的外接球的体积是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eefdcd39676298f214654051fc51ba92.png)
您最近一年使用:0次
2023-07-28更新
|
587次组卷
|
2卷引用:安徽省宣城市2022-2023学年高一下学期期末调研测试数学试卷
解题方法
9 . 如图所示的多面体
中,
是等边三角形,平面
平面
,平面
平面
.
(1)求证:
//平面
;
(2)若
,求多面体
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9142a8490de14a87eda628ffa7e28982.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/309426bb62d195dc56d2ec3fa3f4e2a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17580410bf63dba4fe164265afaac4cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39282bdf319f30d7bc261e2e3ab3b1e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/1/e2a4e0dd-7873-4744-a000-1dea6bc7f5c2.png?resizew=181)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9142a8490de14a87eda628ffa7e28982.png)
您最近一年使用:0次
10 . 在如图所示的几何体中,底面
是正方形,四边形
是直角梯形,
,
,平面
平面
,
分别为
的中点,
,
.
平面
;
(2)求多面体
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c9854839f8f7fe792cd83cf3aa8b093.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b137f02d1323fe46ce853f662542d2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/160ccfe256fc5347daa5e4cc26719512.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e675e59fa66ecdf14ba695e5e649222.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fadb75d3985c7cf99cc8e794ae2d7b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86a8a140610df89623519116d9e9697c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca5a9a04de2ddcec2b2799ab5476f2c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa3d5158341e73d86b6308be42a22fd1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1fd975b889bfe7ddcec0de56b6f23ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c9854839f8f7fe792cd83cf3aa8b093.png)
(2)求多面体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bab155dd2cd44b7301963056f9b0444b.png)
您最近一年使用:0次
2023-07-27更新
|
271次组卷
|
2卷引用:福建省三明市2022-2023学年高一下学期期末质量检测数学试题