作业帮sat2数学求解a plane cuts through a cube in such a way that the plane passes through three of the cube's vertices, no two of which lie on the same edge. if the edge of the cube has a length of 1, what is the surface area of the smaller fragment of
来源：学生作业帮助网 编辑：作业帮 时间：2024/04/29 16:30:59
sat2数学求解a plane cuts through a cube in such a way that the plane passes through three of the cube's vertices, no two of which lie on the same edge. if the edge of the cube has a length of 1, what is the surface area of the smaller fragment of
sat2数学求解
a plane cuts through a cube in such a way that the plane passes through three of the cube's vertices, no two of which lie on the same edge. if the edge of the cube has a length of 1, what is the surface area of the smaller fragment of the cube?
a, 2.4
b 2.7
c 3.1
d 3.7
e 4.3
求过程
sat2数学求解a plane cuts through a cube in such a way that the plane passes through three of the cube's vertices, no two of which lie on the same edge. if the edge of the cube has a length of 1, what is the surface area of the smaller fragment of
很明显三个顶点不共面则切面是正三角形,
较小的部分是一个四面体,三个面为等腰直角三角形,面积为1/2,
另一个面试正三角形,边长√2,面积√3/2
总面积3*1/2+√3/2=2.366
选A