Geometry question

Hi Prerna,

Mitch's solution correctly explains the math behind this question, so I won't rehash it here. I will add a few details to what Mitch did with his approach though.

First, when dealing with a "rectangular solid" (a box or cube), the longest distance between any two points on the surface of the rectangular solid is actually found by going THROUGH the solid.

eg. Upper-Right-Back corner to Lower-Left-Front corner

You can calculate that distance with this formula:

Sq. Root(Length^2 + Width^2 + Height^2)

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In this question, all 3 dimensions of the cube are 10, so the diagonal through the cube = Sq.Root(10^2 + 10^2 + 10^2) = Sq.Root(300) = 10√3.

Since the sphere was inscribed in the cube, the middle of the sphere is also the middle of the cube. Also, the diameter of the sphere = side length of the cube = 10. Thus, the sphere's radius = 5.

So we can subtract the radius of the sphere (5) from from half the diagonal line (5√3) to find the length from the corner to the sphere. The answer choices expect us to factor out a 5.

GMAT assassins aren't born, they're made,
Rich