解题方法
1 . 如图,多面体
的直观图及三视图如图所示,
,
分别为
,
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/9/1d19d4b9-0499-4dd9-8a26-40e6cf7c4bf6.png?resizew=256)
(1)求证:
平面
;
(2)求多面体
的体积;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32c2b716be9d3fce8b00f088e3c4be55.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/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/9/1d19d4b9-0499-4dd9-8a26-40e6cf7c4bf6.png?resizew=256)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7592c4f01c8e06c7ee90df5b9413a9f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b32c05247f6998d7a70d31d13be4148c.png)
(2)求多面体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/982623c6129dd4c535b374c3526d93a6.png)
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名校
解题方法
2 . 如图,三棱锥
及其正视图与俯视图如图所示.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/1/c32c6e98-b0c0-4741-bb35-7f8aba46eb4f.png?resizew=136)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/1/c58890d6-8760-49f0-859d-ce0e19e3c147.png?resizew=187)
(1)求证:
;
(2)求
点到平面
的距离
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/1/c32c6e98-b0c0-4741-bb35-7f8aba46eb4f.png?resizew=136)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/1/c58890d6-8760-49f0-859d-ce0e19e3c147.png?resizew=187)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1e4b16c2c6c9bd089da78122e9d2511.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
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3 . 如图所示的多面体,其正视图为直角三角形,侧视图为等边三角形,俯视图为正方形(尺寸如图所示),E为PA的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/24/9a3621b5-7c5d-4944-a868-b8d6147d7e18.png?resizew=274)
(1)求证:
平面EBD;
(2)求二面角
的余弦值.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/24/9a3621b5-7c5d-4944-a868-b8d6147d7e18.png?resizew=274)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b70cef0b79ca64acbb67dc667fc53b3.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02535e1a690ca111ca7a395a1bf48080.png)
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2022-11-21更新
|
121次组卷
|
2卷引用:贵州省六盘水市2021-2022学年高二下学期期末质量监测数学(理)试题
解题方法
4 . 设某几何体及其三视图:如图(尺寸的长度单位:m)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/8/8caf5821-8200-445f-9aaa-6b555410ef53.png?resizew=336)
(1)O为AC的中点,证明:BO⊥平面APC;
(2)求该几何体的体积;
(3)求点A到面PBC的距离.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/8/8caf5821-8200-445f-9aaa-6b555410ef53.png?resizew=336)
(1)O为AC的中点,证明:BO⊥平面APC;
(2)求该几何体的体积;
(3)求点A到面PBC的距离.
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5 . 四面体ABCD及其三视图如图所示,平行于棱AD,BC的平面分别交四面体的棱AB,BD,DC,CA于点E,F,G,H.
![](https://img.xkw.com/dksih/QBM/2021/12/19/2875651129499648/2877167399247872/STEM/e8637003-6ea9-40fd-8563-1bdc1e0a3661.png?resizew=452)
(1)求点D到面ABC的距离;
(2)证明:四边形EFGH是矩形.
![](https://img.xkw.com/dksih/QBM/2021/12/19/2875651129499648/2877167399247872/STEM/e8637003-6ea9-40fd-8563-1bdc1e0a3661.png?resizew=452)
(1)求点D到面ABC的距离;
(2)证明:四边形EFGH是矩形.
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解题方法
6 . 某几何体的三视图如图所示,P是正方形ABCD对角线的交点,G是PB的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/12/02abe4a0-8391-4b55-bbfe-022a54cd3f5a.jpg?resizew=253)
(1)根据三视图,画出该几何体的直观图;
(2)在直观图中,
①证明:PD∥平面AGC;
②证明:平面PBD⊥平面AGC.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/12/02abe4a0-8391-4b55-bbfe-022a54cd3f5a.jpg?resizew=253)
(1)根据三视图,画出该几何体的直观图;
(2)在直观图中,
①证明:PD∥平面AGC;
②证明:平面PBD⊥平面AGC.
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解题方法
7 . 如图所示的三个图中,上面的是一个长方体截去一个角所得多面体的直观图,它的正视图和侧视图在下面画出(单位:
)
![](https://img.xkw.com/dksih/QBM/2021/1/26/2644412494487552/2645966217216000/STEM/9ff942c10d2f41efb82eebf38c2e5384.png?resizew=224)
(1)按照给出的尺寸,求该多面体的体积;
(2)在所给直观图中连接
,证明:
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9efa9fbcfb9595e2f031aa691db4564b.png)
![](https://img.xkw.com/dksih/QBM/2021/1/26/2644412494487552/2645966217216000/STEM/9ff942c10d2f41efb82eebf38c2e5384.png?resizew=224)
(1)按照给出的尺寸,求该多面体的体积;
(2)在所给直观图中连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e0f0ccc8492a0ccf1eee24867060643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b48596fab810f292e000dfa6284cca9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffe8a84ca3a13f82aff1a022edc66065.png)
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2021-01-28更新
|
105次组卷
|
2卷引用:安徽省安庆市怀宁县第二中学2020-2021学年高三上学期第五次月考数学(文)试题
8 . 已知四棱锥
的直观图如图所示,其中
,
,
两两垂直,
,且底面
为平行四边形.
![](https://img.xkw.com/dksih/QBM/2020/1/16/2378483504398336/2378857983524864/STEM/237b36ce72af4782ae9239c9e2a1d8e8.png?resizew=293)
(1)证明:
.
(2)如图,网格纸上小正方形的边长为1,粗线画出的是该四棱锥的正视图与俯视图,请在网格纸上用粗线画出该四棱锥的侧视图,并求四棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf2e356de1dec9ce998366a1a35c0a9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/2020/1/16/2378483504398336/2378857983524864/STEM/237b36ce72af4782ae9239c9e2a1d8e8.png?resizew=293)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b07e317ffe7859e81b42ef4970e344a.png)
(2)如图,网格纸上小正方形的边长为1,粗线画出的是该四棱锥的正视图与俯视图,请在网格纸上用粗线画出该四棱锥的侧视图,并求四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
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2020-01-17更新
|
213次组卷
|
9卷引用:山西省2019-2020学年高二上学期期中数学(文)试题
山西省2019-2020学年高二上学期期中数学(文)试题辽宁省葫芦岛协作校2019-2020学年高三上学期第二次考试 数学(文) 试题辽宁省葫芦岛协作校2019-2020学年高三上学期第二次考试 数学(理)试题湖南省衡阳市衡阳县、长宁、金山区2019-2020学年高三上学期12月联考数学(文)试题湖南省衡阳市衡阳县、长宁、金山区2019-2020学年高三上学期12月联考数学(理)试题山西省2019-2020学年高二上学期期中考试数学(理)试题(已下线)2020届高三12月第01期(考点07)(文科)-《新题速递·数学》2020届湖南省百所重点高中高三12月大联考数学文科试题2020届湖南省百所重点高中高三12月大联考数学理科试题
名校
9 . 四面体
及其三视图如图所示,平行于棱
,
的平面分别交四面体的棱
,
,
,
于点
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/5/bb359534-3808-45e1-a9eb-9ef1a8c00013.png?resizew=375)
(1) 求四面体
的体积;
(2)证明:四边形
是矩形.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9abaeba15f3abdd877bc701af52c5cd9.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/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/5/bb359534-3808-45e1-a9eb-9ef1a8c00013.png?resizew=375)
(1) 求四面体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)证明:四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/611f100dcfa7803db6eb233e2e7f2dab.png)
您最近一年使用:0次
2019-12-28更新
|
125次组卷
|
7卷引用:2015-2016学年江西省上高县二中高二上学期第一次月考数学试卷
10 . 如图,在四棱锥
中,底面为正方形
,
底面
,该四棱锥的正视图和侧视图均为腰长为6的等腰直角三角形.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/28/2b9e2960-7902-4f0f-9ca2-247f0f2a1596.png?resizew=217)
(1)画出相应的俯视图,并求出该俯视图的面积;
(2)求证:
;
(3)求四棱锥
外接球的直径.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5f1897a7e856b42f8cee0f286ad913d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/28/2b9e2960-7902-4f0f-9ca2-247f0f2a1596.png?resizew=217)
(1)画出相应的俯视图,并求出该俯视图的面积;
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b8e49d68afab33806a63d25a0861c7c.png)
(3)求四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
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