MGMAT Cat Math Practice question

[dloreanbell]

A sphere is inscribed in a cube with an edge of 10. What is the shortest possible distance from one of the vertices of the cube to the surface of the sphere?

10(square root 3 - 1)

5

10(square root 2 - 1)

5( square root 3- 1) Right answer

5( square root 2- 1)

The source is MGMT practice CAT Exam.

I am mostly troubled with how the shortest distance from the sphere surface to the vertices of a cube equals half of the sphere's radius minus 5. What principle am I missing and algebraically how does that solution work?

[dloreanbell]

I actually figured it out. The explanation on the Cat exam is confusing. You subtract the cube diagonal from the sphere diameter. You divide that by 2 to get the shortest distance.

[RonPurewal]

I actually figured it out. The explanation on the Cat exam is confusing. You subtract the cube diagonal from the sphere diameter. You divide that by 2 to get the shortest distance.

Yep, that's how it's done. Basically, you have to imagine a line originating from the corner of the cube and heading directly toward the center of the sphere.