The surface distance between 2 points on the surface of a cube is the length of the shortest path on the surface of the cube that joins the 2 points. If a cube has edges of length 4 centimeters what is the surface distance, in centimeters, between the lower left vertex on its front face and the upper right vertex on its back face?
8
4 ~$\sqrt{5}$~
8~$\sqrt{2}$~
12~$\sqrt{2}$~
4~$\sqrt{2}$~ +4
surface距离,而非直线距离,想象将两个正方形平面展开
https://gmatclub.com/forum/the-surface-distance-between-2-points-on-the-surface-of-a-cube-is-the-305873.html
【引用】
把立方体想象成一个纸盒子,把纸盒子拆开变形成一个整体,整体形状似十字架,题目中所说的前左下角为十字架的左下角,而题目中所说的后上角为十字架正中间的那个正方形的右上角,将两点连直线,形成一个直角三角形,直角的两个角对应的其中一个底边为4cm,而另一个为(4+4)cm,所求为 h^2 = (4)^2 + (4 + 4)^2, h = 4 (sqr 5)
注意surface距离不是直线距离!
想象将两个正方形平面展开