如图为一简单组合体，其底面ABCD为正方形，PD⊥平面ABCD，EC∥PD，且PD=AD=2EC=2．（1）请画出该几何体的三视图；（2）求四棱锥B﹣CEPD的体积．_刷题宝

题干

如图为一简单组合体，其底面ABCD为正方形，PD⊥平面ABCD，EC∥PD，且PD=AD=2EC=2．

（1）请画出该几何体的三视图；

（2）求四棱锥B﹣CEPD的体积．

上一题下一题 0.0难度选择题更新时间:2016-09-05 03:41:24

答案(点此获取答案解析）

解：（1）该组合体的主视图和侧视图如图示：

（2）∵PD平面ABCD，PD⊂平面PDCE

∴平面PDCE⊥平面ABCD

∵BC⊥CD

∴BC⊥平面PDCE（5分）

∵S_PCDE=

1

2

（PD+EC）•DC=3

∴四棱锥B﹣CEPD的体

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