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
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![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](/uploads/image/z/5090784-24-4.jpg?t=sat2%E6%95%B0%E5%AD%A6%E6%B1%82%E8%A7%A3a+plane+cuts+through+a+cube+in+such+a+way+that+the+plane+passes+through+three+of+the+cube%27s+vertices%2C+no+two+of+which+lie+on+the+same+edge.+if+the+edge+of+the+cube+has+a+length+of+1%2C+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
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