Question

In a cube with edge length $2$, calculate the distance from the center of one face to a vertex of the opposite face.

• A. $2.00$
• B. $2.24$
• C. $2.45$
• D. $2.65$

Answer 1

The correct option is C $2.45$

Distance between center of one face to center of opposite face is $2$.
Distance from center of face to vertex is $2\sqrt{2}/2=\sqrt{2}$.
Therefore, distance from the center of one face to a vertex of the opposite face is $\sqrt{2^2+{\sqrt{2}}^2}=\sqrt{4+2}=\sqrt{6}=2.45$