When approaching this problem I noticed that the sphere touches the six edges of the box. This means I don't need additional information about the box as I already knew the radius. I also noted that calculating the distance between the center of the sphere and the corner of the box is the same thing as calculating the diagonal of a cube with each side equal to one radius of the sphere).
Given the radius of 2 I calculate the diagonal of the cube with side length 2. As the formula for the diameter of a cube is "side length*sqrt(3)". The answer had to be C. (sidelength = 2 was given in q-stem)
It would be interesting to see a question such as this one, where the test makers leave room at the top and the bottom but allow the sphere to be tangent to the up-right sides. This could likely be used in a data sufficiency question in different ways. Does anyone know about any questions like the one I described?
Best wishes.
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I love being wrong. An incorrect answer offers an extraordinary opportunity to improve.