名校
解题方法
1 . 正三棱柱
的底面正三角形的边长为
为
的中点;
.![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
平面
;
(2)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca1ebdf74ee45f3736307d4a7e64717f.png)
(3)求
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c1bd8a678857b47bb627e665ce58df5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8d927585a17c2e98ef7d5a9589a26ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ba9e20d667d04bf3ee7f55cc795ce01.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca1ebdf74ee45f3736307d4a7e64717f.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41104641f3e2260d00aeadf8fb8a078a.png)
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解题方法
2 . 如图,在直三棱柱
中,点D为线段AC的中点.
平面
;
(2)若
,
,
,求
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac5ea494bb75a5c04e61c9e32aceabc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7935fe3125f247b7bea4f065ce9ad985.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55a2310cbba5e050488cd9296eb195d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/834b1e9c904906c46d4f69e3b7765b40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7935fe3125f247b7bea4f065ce9ad985.png)
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3 . 如图,四棱锥
中,
底面ABCD,底面ABCD是正方形,
,点M是棱PC的中点.
平面ABCD;
(2)求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f83a04565a8ebaa111894b724b0ba266.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa7084fef1f20c7af36659c1faa643ca.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8ca90486f5edcf87de3cd818fc9189a.png)
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4 . 在直三棱柱
中,
,
,
.
(1)求直三棱柱
的体积;
(2)求直三棱柱
的表面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/883fc5e3faf39829d60804b59deb1730.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ef8866ccf160ddc441bf69c5d3a3d5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/259414bba09b088ca98ed4c3fcee8197.png)
(1)求直三棱柱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
(2)求直三棱柱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
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5 . 如图,三棱柱
内接于一个圆柱,且底面是正三角形,圆柱的体积是
,底面直径与母线长相等.
(2)求三棱柱
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35e2d7c958e99bcd9d7f251c19ee3544.png)
(2)求三棱柱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
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2024·全国·模拟预测
解题方法
6 . 如图,在三棱台
中,
平面
,
为等腰直角三角形,
,
分别为
的中点.
平面
;
(2)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ccc0d735dc14c92a8926d9b1def6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc9d0b66cbe64cf35e27a6c58fba3691.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80bbe13f5c674ba211bc31948cc91151.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c22b298568f56a12dba91be6f8f004c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e870b8ed9f3df43c140946603f0243c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2717942007242a7d0c242f274e8b224f.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cc6184b191e6da43911e701121517e.png)
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名校
解题方法
7 . 几何体ABCDEF中,平面ADE、平面BCF和平面ACFE均与平面ABCD垂直,且
,
,
,
.
;
(2)求四棱锥
与四棱锥
公共部分的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/940078c89bad1724a5d7006a54755398.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d364ece0e03ccd9221e3c6ee6f1634cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10df84d553a8826a7ce9bff4bf0d95b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45a0a5049cfbc5292060fdc736f6fe1f.png)
(2)求四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80c753cb1eb73fd8d136d00462970797.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e5ba482836565abad208665cf7b9972.png)
您最近一年使用:0次
名校
解题方法
8 . 在直三棱柱
中,
,侧棱长为3,侧面积为
.
的体积;
(2)若点D、E分别在三棱柱的棱
上,且
,线段
的延长线与平面
交于
三点,证明:
共线.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b42eeaa3e80a1e0f298a175bcc0e45e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afaf8822d03a1bc2fa3d8700082e3511.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78b083008d31d3f029aa40dbf2a6a1d3.png)
(2)若点D、E分别在三棱柱的棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac3d169c28e3a2cdb9abf322244609d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1699518dd0e565c44cfe7c6318aff824.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc9e58ac8c84d836aa006a70b20773d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7a8f3a13cb258c61e2a221c2bf09979.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7a8f3a13cb258c61e2a221c2bf09979.png)
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9 . 如图,已知点
在圆柱
的底面圆
上,
为圆
的直径,
,
,三棱锥
的体积为
.
的表面积;
(2)求三棱锥
外接球的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192f4f9446c954a291f779d963f90257.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/9774f83067ed956a551bc41adcce0469.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9cb9ef4d25a34b2230607d6ba4ab103.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5495a154d006c33979813b86924dc0f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37fbbc8f521edab89a7e373287bcfbd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192f4f9446c954a291f779d963f90257.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5495a154d006c33979813b86924dc0f9.png)
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10 . 某广场设置了一些石凳供大家休息,这些石凳是由棱长为
的正四面体沿棱的三等分点,截去四个一样的正四面体得到.
(2)为了美观工人准备将石凳的表面进行粉刷,已知每平方米造价50元,请问粉刷一个石凳需要多少钱?(
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dba70cedec21ecbc446a7d53de3b32ff.png)
(2)为了美观工人准备将石凳的表面进行粉刷,已知每平方米造价50元,请问粉刷一个石凳需要多少钱?(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/460317e7c26f95b9b29cfe1a89b796d6.png)
您最近一年使用:0次