A cubic box with an edge length of 4 inches holds a ball

Please refer the fig.
diagonal = √3a------>4√3
so half upto centre=2√3
Ans C

Experts please move the question in PS section...

The distance between the center of the ball and a corner of the box is in fact half the long diagonal of this cube.

Long diagonal of a cube = s√3

so long diagonal of this particular cube is 4√3, half of which is 2√3, so C is the right answer.

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.

Dear Moderator ,
Found this PS question in the DS section of geometry, hope you will look into this. Thank you.

______________
Moved to PS forum. Thank you.

Question seems much harder than it actually is.


If you step back and think Symmetrically about the Picture --- Since it is a Cube and the Sphere/Ball in the Cube is tangent to Each Congruent Face/Side, then the Center of the Cube and the Center of the Sphere will be COMMON.

Therefore, the Distance from the Center of the Ball/Center of the Cube to 1 of the Vertices of the Cube will =

1/2 * (Main Diagonal through the Center of the Cube) =

1/2 * sqrt[ (4)^2 + (4)^2 + (4)^2 ] =

1/2 * sqrt[ (16) * (3)]

4/2 * sqrt[ 3 ]

2 * sqrt(3) = 1/2 the Main Diagonal of the Cube

-C-

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