swerve wrote: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?

A. 8
B. 4\(\sqrt{5}\)
C. 8\(\sqrt{2}\)
D. 12\(\sqrt{2}\)
E. 4\(\sqrt{2}\) + 4

The OA is B

Source: Official Guide

The distance between the lower-left vertex on its front face and the upper right vertex on its back face is the longest diagonal of the cube; however, this is not the surface distance. The question defines surface distance as the 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.

To find the shortest distance (surface distance) between the diagonal points of the cube, unfold the cube.
You will observe the base and right side face of the cube as a rectangle of length = 4 + 4 = 8 cm and height = 4 cm

Shortest distance (surface distance) = Distance along the diagonal of the rectangle

= √(8^2 + 4^2)
= 4√5

The correct answer: B

Hope this helps!

-Jay
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