1/5单选题
难度：
1.
如图,有一个水平放置的透明无盖的正方体容器,容器高8cm,将一个球放在容器口,再向容器内注水,当球面恰好接触水面时测得水深为6cm,如果不计容器的厚度,则球的体积为（ ）
| A |
|
| B |
|
| C |
|
| D |
|
- 提示1：
- PHA+55CD55qE5oiq6Z2i55qE5oCn6LSoPC9wPg==
- 提示2：
- PHA+55CD55qE5L2T56ev5YWs5byPPGltZyBzcmM9Imh0dHBzOi8vcDEucWluZ2d1by5jb20vRzEvTTAwL0FBL0U5L3JCQUNGRlRKelZuQ2psTzZBQUFDR2tmTlN6MDQ5MS5wbmciIGRhdGEtY2tlLXNhdmVkLXNyYz0iaHR0cHM6Ly9wMS5xaW5nZ3VvLmNvbS9HMS9NMDAvQUEvRTkvckJBQ0ZGVEp6Vm5DamxPNkFBQUNHa2ZOU3owNDkxLnBuZyIgaGVpZ2h0PSI0MiIgd2lkdGg9IjY3Ij48L3A+
正确答案：QQ==
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
2/5单选题
难度：
2.
已知正方体外接球的体积是
，那么正方体的棱长等于（ ）
| A |
|
| B |
|
| C |
|
| D |
|
- 提示1：
- PHA+5qC55o2u55CD55qE5L2T56ev5YWs5byP5rGC5Ye65Y2K5b6EPC9wPg==
- 提示2：
- PHA+5om+5Ye65q2j5pa55L2T55qE5qOx6ZW/5LiO55CD55qE5Y2K5b6E5LmL6Ze055qE5YWz57O777yOPC9wPg==
正确答案：RA==
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
3/5单选题
难度：
3.
将边长为1的正方形以其一边所在直线为旋转轴旋转一周，所得几何体的侧面积为（ ）
| A |
|
| B |
|
| C |
|
| D |
|
- 提示1：
- PHA+56Gu5a6a5peL6L2s5L2T55qE5b2i54q25Li65ZyG5p+xPC9wPg==
- 提示2：
- PHA+5ZyG5p+x55qE5L6n6Z2i5bGV5byA5Zu+PC9wPg==
正确答案：Qw==
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
4/5单选题
难度：
4.
若三棱锥的三个侧面两两垂直，且侧棱长均为
，则其外接球的表面积为（ ）
| A |
|
| B |
|
| C |
|
| D |
|
- 提示1：
- PHA+5bCG5LiJ5qOx6ZSl5aSN5Y6f5Li65q2j5pa55L2TPC9wPg==
- 提示2：
- PHA+5q2j5pa55L2T55qE5L2T5a+56KeS57q/5piv5YW25aSW5o6l55CD55qE55u05b6EPC9wPg==
- 提示3：
- PHA+5Yip55So55CD55qE6KGo6Z2i56ev5YWs5byP55u05o6l5rGC5b6XLjwvcD4=
正确答案：Qw==
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
5/5单选题
难度：
5.
点A，B，C，D在同一个球面上，
，AC=2，若球的表面积为
，则四面体ABCD体积最大值为（ ）
| A |
|
| B |
|
| C |
|
| D | 2 |
- 提示1：
- PHA+55S75Zu+5YiG5p6QPC9wPg==
- 提示2：
- PHA+5p6E6YCg5Z6C5b6E5a6a55CG5LiJ6KeS5b2iPC9wPg==
正确答案：Qw==
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