名校
解题方法
1 . 如图,S为圆锥顶点,O是圆锥底面圆的圆心,AB、CD为底面圆的两条直径,
,且
,
,P为SB的中点.
平面PCD;
(2)求圆锥SO的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38a5ed40e239098309bb3c9a5ad28489.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cea06e3edaaef607d8b78ecf4090d07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8825d400f453c5c17a7beeb1cc9a9cf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1ea0adc03fc8ba355dbdac586f4b707.png)
(2)求圆锥SO的体积.
您最近一年使用:0次
2023-08-02更新
|
2408次组卷
|
5卷引用:陕西省渭南市富平县2020-2021学年高一上学期期末数学试题
陕西省渭南市富平县2020-2021学年高一上学期期末数学试题贵州省遵义市南白中学2023-2024学年高二上学期第一次联考数学试题新疆阿拉山口市中学2023-2024学年高二上学期开学考试数学试题广东省普通高中2024届高三合格性考试模拟冲刺数学试题(二)(已下线)第13章 立体几何初步 单元综合检测(重难点)-《重难点题型·高分突破》(苏教版2019必修第二册)
2023·河北·模拟预测
名校
解题方法
2 . 如图,用一垂直于某条母线的平面截一顶角正弦值为
的圆锥,截口曲线是椭圆,顶点A到平面的距离为3.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/7/030c760c-c753-4169-b610-21ab5b11bd12.png?resizew=181)
(1)求椭圆的离心率;
(2)已知P在椭圆上运动且不与长轴两端点重合,椭圆的两焦点为
,
,证明:二面角
的大小小于
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7294f5ae2a24ff42e84cd9773b2a7287.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/7/030c760c-c753-4169-b610-21ab5b11bd12.png?resizew=181)
(1)求椭圆的离心率;
(2)已知P在椭圆上运动且不与长轴两端点重合,椭圆的两焦点为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c29eadbcfaf2fb50b07d0f5fa165a0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
您最近一年使用:0次
解题方法
3 . 在
中,
的中点为
,把
绕
旋转一周,得到一个旋转体.
(1)求旋转体的体积;
(2)设从
点出发绕旋转体一周到达
点的最近路程为
,探究
与
的大小,并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/226fdcba5527912ee7d4c32eb74d7245.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
(1)求旋转体的体积;
(2)设从
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6682956839817dd487ede5cbfc50f710.png)
您最近一年使用:0次
解题方法
4 . 如图,已知一个圆柱和一个圆锥等底等高,点O为底面的圆心,点P为圆锥的顶点.若圆柱的高等于它的底面直径.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/5/5a56faf6-7614-489a-8491-7a2626252eb7.png?resizew=250)
(1)求证:圆柱的任意一条母线和圆锥的任意一条母线所成的角都相等;
(2)求圆柱的表面积和圆锥的表面积的比值.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/5/5a56faf6-7614-489a-8491-7a2626252eb7.png?resizew=250)
(1)求证:圆柱的任意一条母线和圆锥的任意一条母线所成的角都相等;
(2)求圆柱的表面积和圆锥的表面积的比值.
您最近一年使用:0次
5 . 如图,在
中,
,斜边
,现将
绕AC旋转一周得到一个圆锥,BD为底面圆的直径,点P为圆锥的内切球O与CD的切点,
为圆锥底面圆周上异于B,D的一点.
![](https://img.xkw.com/dksih/QBM/2022/1/21/2899096901861376/2909066567385088/STEM/1d4def76-13cf-4a3e-b978-c387907a7275.png?resizew=259)
(1)求证:
平面
;
(2)当
时,求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd967903ed5a6f640a5b801ec8be0070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/564e238659b316ab3275829470ce0c89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65a3e478bb87d094e3a0af30dd10ae8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd967903ed5a6f640a5b801ec8be0070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://img.xkw.com/dksih/QBM/2022/1/21/2899096901861376/2909066567385088/STEM/1d4def76-13cf-4a3e-b978-c387907a7275.png?resizew=259)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/373f735f0f04d11f1951eaef1bb78b6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/113c87d7b997847259f17ee8576ee44c.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/295aced98768ce261e00fe6660a427a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9655de237e97442f6920fad144b2d85b.png)
您最近一年使用:0次
6 . 已知圆台的上、下底面半径分别为20cm,30cm,高为18cm,过它的两条母线作一平面截去上底面圆周的
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/17/6b6850c8-64d3-441b-88cd-4b150e95f519.png?resizew=220)
(1)求证:这个截面截下底面圆周也是
;
(2)求这个截面面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56d266a04f3dc7483eddbc26c5e487db.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/17/6b6850c8-64d3-441b-88cd-4b150e95f519.png?resizew=220)
(1)求证:这个截面截下底面圆周也是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56d266a04f3dc7483eddbc26c5e487db.png)
(2)求这个截面面积.
您最近一年使用:0次
名校
解题方法
7 . 圆锥的顶点为
,底面圆心为
,线段
是圆
的直径,点
是圆
上异于
、
的点,
垂直于圆
所在的平面,且
,
.
(1)若
为线段
中点,求证:
平面
;
(2)求圆锥的侧面积,并求三棱锥
体积的最大值;
(3)当三棱锥
体积最大时,点
沿圆锥表面运动到母线
中点
,求该点经过的路线的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.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/ef49a3ca580a144cc65a609c167facc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a9b5996067a3fc9adcf0ca178dddf03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94c80b508a551c7e67587eaf6eaae2df.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e56fdf217165748fafe938b64fa08179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bdac31e82ed00eace31e8c075c97bb2.png)
(2)求圆锥的侧面积,并求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
(3)当三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
您最近一年使用:0次
名校
解题方法
8 . 如图所示,线段AB为圆锥SO的底面圆的直径,C为底面圆周上异于A,B的动点,点P为AC的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/24/f1fc38f4-131c-4e68-8358-214576a6d1ad.png?resizew=173)
(1)证明:平面
平面SOP
(2)若
,圆锥SO的母线与底面圆所成的角为60°,求三棱锥
的体积最大时,平面SOP与平面SBC所成的锐二面角的余弦值
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/24/f1fc38f4-131c-4e68-8358-214576a6d1ad.png?resizew=173)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3559df13766ca6e72ab355be51c93804.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20f9725db739ef914670f1524093f36b.png)
您最近一年使用:0次
2021-11-26更新
|
445次组卷
|
4卷引用:河北省衡水市冀州区第一中学2021-2022学年高二上学期期中数学试题