14. 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?

5 (√3 - 1)

Step-by-step explanation:

Edge of cube = 10

If the sphere is inscribed in a cube, the edges of the cube is equal to the diameter of the sphere.

Diameter = 10

We will then find the diagonal of the cube.

Diagonal = √10^2 + 10^2 + 10^2

= √300

= 10√3

Let X be the distance between the vertex of the cube and the surface of the sphere

X = (diagonal - diameter) / 2

X = (10√3 - 10) / 2

X = (10 (√3 - 1)) / 2

X = 5 (√3 - 1)