1 . 如图,
是圆柱的母线,线段
的两个端点分别在圆柱的两个底面圆周上,它与圆柱的轴
所成的角为
,且
,轴
到平面
的距离为3,求此圆柱的侧面积及体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192f4f9446c954a291f779d963f90257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6b86c22b670a8e9f3896f9e8883fbbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c1b51460d650925240e40bd91911ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192f4f9446c954a291f779d963f90257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ef671ff46a372d5351b8c2f9eb26b48.png)
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解题方法
2 . 圆柱的高为4厘米,底面半径为3厘米,已知上底面一条半径
所在直线与下底面的一条半径
所在直线的夹角为60°,求:
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/16/97fb6829-9de9-4d25-9650-cd7fae970c4b.png?resizew=106)
(1)直线
与圆柱的轴
所成角的正切值;
(2)线段
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6637859805b7b01f7a9a64771563406e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/16/97fb6829-9de9-4d25-9650-cd7fae970c4b.png?resizew=106)
(1)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/943712a5e96b16cc15d775cc4687237e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/270ddac9587bf1ea553914cb69595ab2.png)
(2)线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/943712a5e96b16cc15d775cc4687237e.png)
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3 . 已知两条异面直线a,b所成角为
,距离为d,两直线上分别取点E、F.
,
,M、N分别为公垂线与a、b的交点,
,
.求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411768ff69e9034dd487de83f7ea97c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2763fdfc8ee8b0efaf2f1b1c181ffa7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1bb6beca539b2aad1a04b93ff58bd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c577c79eacdb7e00270704e5c0336bce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ee975978fd2a3d73a3ba8e2f8ac99fa.png)
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4 . 设两条电线所在的直线是异面直线,它们的距离是2 m,所成的角是60°.已知这两条电线上各有一点,距离公垂线的垂足都是8 m.求这两点之间的距离.
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5 . 若两条异面直线a、b所成的角为
,它们的公垂线段
,长为d,E、F两点分别在直线a、b上,且线段AE长为m,线段
长为n.求线段EF的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6024fd4532f5f981deac4582c799a6ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d71fe246270d1277f9eb2bf15af22e83.png)
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