解题方法
1 . 正方体
的棱长为
,
分别为
上的点,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bac8911246624118ff506edd4eb14e9.png)
,
分别为
上的动点.若点
在同一球面上,当
平面
时,该球的表面积为 ______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3304e23f3b0f9569c4140ca89b6498.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3657e945e364488df6ba6922d6a25229.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bac8911246624118ff506edd4eb14e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0204f76cda5ea4ced714588be1efeaa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36080e182835de5da4c2d016fd40bf49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3ec0cf152e35708d87a83cb4cb56461.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b61346bd4091070ba84a4046f87f365.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a8035fc825a001d7d9a3dacd8271662.png)
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2 . 圆台内有一个球,该球与圆台的侧面和上下底面均相切,球的球心为
.已知圆台上底面圆的半径为1,下底面圆的半径为
,母线与底面所成的角为
,且
.若该圆台的上下两个底面都在同一个球的球面上,该球的球心为
,记圆台的表面积为
,体积为
,球
的表面积为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad83973d1361b2928c7e783ffd073b75.png)
______ ,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90a3587375b61aba9c85c469e40f5148.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acd15bcd2eda1d7a943170b39a94a54a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da19f0d43a33b280c90491d999ce8227.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12fe32dfbd66709875c5b9f79c9496da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be54e84508decfcce6d2fcbe6c8c1a92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12fe32dfbd66709875c5b9f79c9496da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/150a135bbd528daf3f19a58a621a57c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad83973d1361b2928c7e783ffd073b75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90a3587375b61aba9c85c469e40f5148.png)
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解题方法
3 . 已知四面体
的各顶点都在同一球面上,若
,平面
平面
,则该球的表面积是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/064b57e4a36cf0d69a0297f6f7c20114.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcf6dc837ae85207789b94d109c5c2eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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4 . 如图,在水平放置的圆柱内,放入三个半径相等的实心小球
(小球材质密度
),小球
分别与上底面、下底面相切,小球
与圆柱壁相切,且
在轴截面中,向圆柱内注满水,水面刚好淹没小球
,若圆柱底面半径为
,则球
的体积为_______ ,圆柱的侧面积与球
的表面积的比值为_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a775d4bbc6b8d9201e0d8add10a9a84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/098a3e7d1f1890863b7483a98b618119.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb8fb6f3d7540831a9e97d3b184a491.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
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5 . 球面被平面所截得的一部分叫做球冠,截得的圆叫做球冠的底,垂直于截面的直径被截得的一段叫做球冠的高.球被平面截下的一部分叫做球缺,截面叫做球缺的底面,垂直于截面的直径被截下的线段长叫做球缺的高,球缺是旋转体,可以看做是球冠和其底所在的圆面所围成的几何体.如图1,一个球面的半径为
,球冠的高是
,球冠的表面积公式是
,与之对应的球缺的体积公式是
.如图2,已知
是以
为直径的圆上的两点,
,则扇形
绕直线
旋转一周形成的几何体的表面积为__________ ,体积为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eabd5f3a86afe49dcd70571e2b96cfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aef5e6ee09edc8b6e274cd45a2e7af02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d24f6e152f122a7b0c7b72cd40429fda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f784040120239d7e75c591029d56c31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bf126cfed85fa9b7720ec6f7b0008dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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2024-03-10更新
|
1266次组卷
|
4卷引用:山东省泰安市新泰第一中学2024届高三下学期高考模拟测试(一)数学试题
山东省泰安市新泰第一中学2024届高三下学期高考模拟测试(一)数学试题山东省临沂市2024届高三下学期一模考试数学试题(已下线)第六章 突破立体几何创新问题 专题二 融合科技、社会热点 微点3 融合科技、社会热点等现代文化的立体几何和问题综合训练【培优版】(已下线)高一 模块3 专题1 小题进阶提升练
名校
6 . 腰长为
的等腰
的顶角为
,且
,将
绕
旋转至
的位置得到三棱锥
,当三棱锥体积最大时其外接球面积为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](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/8d2c413253fe5bc1f9287a35e6fc45eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/661ff55b5ebbadfb600989af3cfce2fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4357d5744046d4d44abb09e1ee35fcb.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/4/83e0a5e8-6b8c-466e-a7ca-ce765288564b.png?resizew=138)
A.![]() | B.![]() |
C.![]() | D.![]() |
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2023-06-03更新
|
901次组卷
|
3卷引用:山东省泰安肥城市2023届高考适应性训练数学试题(三)
7 . 将半径为
,圆心角为
的扇形围成一个圆锥(接缝处忽略不计),则该圆锥的内切球的表面积为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70f5389990c3a0c5373f3bd9fb2454c9.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2023-06-03更新
|
588次组卷
|
2卷引用:山东省泰安肥城市2023届高考适应性训练数学试题(二)
8 . 我国古代《九章算术》将上下两个平行平面为矩形的六面体称为刍童.如图所示的池盆几何体是一个刍童,其中上下底面为正方形,边长分别为6和2,侧面是全等的等腰梯形,梯形的高为
.已知盆中有积水,将一半径为1的实心铁球放入盆中之后,盆中积水深变为池盆高度的一半,则该盆中积水的体积为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/2/9fd6dd13-c19c-4617-a2b7-43cf66ca6db3.png?resizew=131)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/2/9fd6dd13-c19c-4617-a2b7-43cf66ca6db3.png?resizew=131)
A.![]() | B.![]() | C.![]() | D.![]() |
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2023-04-30更新
|
1004次组卷
|
3卷引用:山东省泰安市2023届高三二模数学试题
解题方法
9 . 在正三棱锥
中,底面
是边长为
正三角形,
是
的中点,若直线
和平面
所成的角为
,则三棱锥外接球的表面积为
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91d7502471f2dd73d83782aab1820e3b.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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10 . 如图,四棱锥
的底面为矩形,
底面
,
,且
,则下列结论中不正确 的是( )
![](https://img.xkw.com/dksih/QBM/2022/5/10/2976290565963776/2978056115830784/STEM/4763f3a6684c447c88104f032c31a461.png?resizew=215)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fb2e071d4e01107dcf7d95cbb86b415.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa816ed38cfb504eed6c57e9f7132569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a7dbc702617c765a573961953cc0901.png)
![](https://img.xkw.com/dksih/QBM/2022/5/10/2976290565963776/2978056115830784/STEM/4763f3a6684c447c88104f032c31a461.png?resizew=215)
A.![]() ![]() ![]() ![]() ![]() |
B.![]() ![]() ![]() |
C.![]() ![]() ![]() |
D.四棱锥的外接球的表面积的最小值是![]() |
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