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?

1. 8
2. 4√5
3. 8√2
4. 12√2
5. 4√2+4

“The surface distance between 2 points on the surface of a cube is the”- is a topic of the GMAT Quantitative reasoning section of GMAT. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

Solution and Explanation:
Approach Solution 1
Letting x = the surface distance between the lower left vertex on its front face and the upper right vertex on its back face; we can create the equation:

x^2 = 4^2 + 8^2
x^2 = 80
x = √80 = 4√5

Correct Answer: B

Approach Solution 2:

To find the Shortest distance between the diagonal points of the cube, we need to unfold the cube completely.

Imagine the base and right side face of the cube into a flat rectangle of length = 8 cm and breadth = 4 cm

Shortest distance = path travelled along the diagonal of the above rectangle

Distance= √8^2+4^2
Distance= 4 √2^2+1^2
Distance= 4√5

Shortest path between AB= √(4^2+8^2)=4√5

Correct Answer: B

Approach Solution 3:

Because of the symmetry

CD= DE = 2
AD^2= 4^2+2^2
AD = \(\sqrt{20}\) = 2√5
BD^2= 4^2+2^2
BD = √20= 2√5
Total distance = AD + BD = 2√5 + 2√5 = 4√5

Correct Answer: B

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