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1 . 如图,在直三棱柱
中,点
,
分别是棱
,
的中点,则下列结论中正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
A.![]() ![]() | B.![]() ![]() |
C.![]() ![]() | D.![]() ![]() |
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2 . 已知圆锥的体积为2,高为3,则其底面半径为( )
A.![]() | B.![]() | C.![]() | D.![]() |
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3 . 如图,矩形
是水平放置的一个平面图形由斜二测画法得到的直观图,其中
,
,则原图形的面积是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14f0b6aa43bf7e390ec965f039896cad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8ec7ad85323f79ebf1dbadb92e09545.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea386d1139b58532dc1194457faadd85.png)
A.20 | B.10 | C.![]() | D.![]() |
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解题方法
4 . 如图,已知
是平行四边形
所在平面外一点,
、
分别是
、
的三等分点(
靠近
,
靠近
);
平面
.
(2)在
上确定一点
,使平面
平面
,并证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7592c4f01c8e06c7ee90df5b9413a9f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b28a07491270be75a3697538bec706.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
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5 . 下列结论正确的是( )
A.圆柱的每个轴截面都是全等矩形 |
B.长方体是直四棱柱,直四棱柱也是长方体 |
C.用一个平面截圆锥,必得到一个圆锥和一个圆台 |
D.四棱柱、四棱台、五棱锥都是六面体 |
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6 . 已知梯形
,按照斜二测画法画出它的直观图
,如图,其中
,
,
,下列说法正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bae2fd0bb6dcb90ee752e7bcabd22b8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e94d7dd65ff87a08471f337df0bd53e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1eb63eab9f3e7554728a72366084d832.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f53836b2ccc010b853d9a82f2e8d1868.png)
A.![]() ![]() | B.![]() |
C.梯形![]() | D.梯形![]() |
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7 . 如图,一个圆柱和一个圆锥的底面直径和它们的高都与一个球的直径
相等,下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e7f30167e1135806fe9de641870b1e6.png)
A.圆柱的侧面积为![]() |
B.圆锥的侧面积为![]() |
C.圆柱的体积等于圆锥与球的体积之和 |
D.三个几何体的表面积中,球的表面积最小 |
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8 . 如下如图,水平桌面
上放置一个透明塑料制成的长方体水槽
,水面高度恰为长方体高的一半,在该长方体侧面
上有一个小孔
点到
的距离为3.将该长方体水槽绕
倾斜(
始终在桌面上,如下如图所示),此时水恰好流出时,液面与棱
分别相交于点
.
是矩形;
(2)当水恰好流出时,求二面角
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5bf350a619ef25d8d9b988f3db804e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56fd0ef94178e7bf9cee5e6982359845.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82b724168afaee2ecddf97257180be18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42f30422880a52311e68cfe78ad6131e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/360a93b9662f0ab8a69b131497520b53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48593b2bdb51550ec0a2b9d5893d36fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/389bc3f29c058067e06e0d0d2be399da.png)
(2)当水恰好流出时,求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82d81cdcae29cd4bbcd3d40800d19933.png)
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解题方法
9 . 如图,已知正方体
的棱长为2,若K为棱
的中点,过A,C,K三点作正方体的截面,则截面的周长为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
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10 . 如图,在正方体
中,
,
,
分别为
,
,
的中点,则以下结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f66fb71b75b63594ebeeeebd1963eed5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab35850dbc661ded6456b70767cc6cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
A.![]() |
B.平面![]() ![]() |
C.![]() ![]() |
D.异面直线![]() ![]() ![]() |
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