The surface distance between 2 points on the surface of a

[BTGmoderatorDC]

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. \(4\sqrt{2} + 4\)



OA B

Source: Official Guide

[deloitte247]

What is the surface distance in centimeters between the lower-left vertex on its front face and the upper right vertex on its back?
i.e What is the distance between the diagonal point of the cube.
If the base and the right side face of the cube is unfolded completely into a rectangle
The length = 4 * 2 = 8 cm
The bread = 4 cm
Remember that the length and breadth of a cube are uniform across all its sides.
Therefore, the path traveled along the diagonal of the rectangle that was unfolded =
$$=\sqrt{l^2+b^2}$$
$$=\sqrt{8^2+4^2}$$
$$=\sqrt{64+16}$$
$$=\sqrt{80}$$
$$=\sqrt{16\cdot5}$$
$$=\sqrt{16}\cdot\sqrt{5}$$
$$=4\sqrt{5}$$

Answer = option B

[Scott@TargetTestPrep]

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. \(4\sqrt{2} + 4\)



OA B

Source: Official Guide

Solution:

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

Answer: B