Question

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?

Answer 1

9.66cm

Explanation:

Given a cube, the Surface Distance between two points is defined as the length of the shortest path on the surface of the cube that joins the 2 points.

For a cube of length 4cm, we are to determine the surface distance between the lower left vertex on its front face and the upper right vertex on its back face.

In the produced diagram,

• The front face is denoted by the square ABCD
• The back face is denoted by square EFGH.
• The distance we are to determine is |AX|.

The shortest distance between A and C is the diagonal that joins point A to point C.

Using Pythagoras theorem,

`|AC|=√(|AB|^2+|BC|^2) \\=√(4^2+4^2)\\=√(32) \\|AC|=4√(2) cm`

Therefore, the shortest distance between A and point X

=|AC|+|CX|

`=4√(2) +4\\=9.66cm`