A cube has vertices at (0,0,0), (2,0,0), (0,2,0), and (0,0,2). What is the distance from the origin to the center of the cube?
Show the answer and explanation
Correct answer
A. √3
Principle or equation
The center of a cube with side length s is at (s/2, s/2, s/2). The distance from the origin is sqrt((s/2)^2 + (s/2)^2 + (s/2)^2) = sqrt(3(s/2)^2) = (s√3)/2.
Why this answer is correct
The side length is 2, so the center is at (1,1,1). Distance = sqrt(1^2 + 1^2 + 1^2) = √3.
Example
For a cube of side 4, center at (2,2,2), distance = sqrt(4+4+4) = 2√3.
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